Tricky 1% Question: In a room of 100, 99% are left-handed. How many left-handed people have to leave to bring that percentage down to 98%? ua-cam.com/video/U6emQxf-cxY/v-deo.html
@@JossWainwright He (teacher) was pissed in the sense that he didnt want to teach that day and therefor gave the class a difficult exercise that would normaly take very long to finish. Or so thats what Ive read
I remember recently I was teaching my kids trapezoid area. It hits me that, you can use the same area formula to solve these addition sequences. Set your first term as Short-base, and last term as Long-base, the height would be number of terms (usually it's just last minus first plus one). And if it is odd/even only sequence, then half the number of terms before plus one, if it's adding every 3rd term, then 1/3 of the number plus one.
@@Ninja20704not realy both are pretty much the same amount of operations with the method the commentor provided being a tiny bit less, also it follows the general formular(better/more similar) for such sums which is n*(n+1)/2 which you can also think of as adding the highst and lowest numbers together will give you allways one more than the highest, multiply this by all numbers and because you decrease the the total sums to half you get the answer. Finding a Formular for n² for example isnt this linear, still not that difficult(more annoying) if you know what to do/for any power of n or sum.
It depends on the usage of the word "between" - they should specify inclusive/exclusive in the question. I'm frequently using the BETWEEN operator in SQL, and it's always inclusive. However, prior to this, I'd always understood "between" to be exclusive.
1 + 2 + 3 + .. + n , can be seen as one half of the number of blocks in an n x n square, if you include also the diagonal. Total number is n^2, so you subtract n for the diagonal, take half and add back in the diagonal: (n^2 - n) x 1/2 + n = 1/2 n^2 + 1/2 n.
Wow, I love how this video simplified the classic math problem. It’s amazing how understanding a simple formula can make such a big difference. Using the formula, the sum from 0 to 100 is 5050, a satisfying math trick that never gets old. Also, shoutout to SolutionInn for making concepts like these easy to practice and revisit.
“Between” 0 and 100 doesn’t include the 0 or the 100. “From” 0 “To” 100 does. What are the whole numbers “Between” 1 and 4? 2 and 3. What are the whole numbers “From” 1 “To” 4? 1, 2, 3 and 4.
Easy: for each value of x < n/2 there is a complement n-x which when added together gives a result of n (n-x+x). This leads to an initial answer of n²/2 which may or may not need a correction depending on whether n is odd or even. If n is odd you keep the answer n²/2, if n is even you add n/2 to the initial result.
great video. I'm trying to brush up on my math after 20 years of being out of school. No real need to, but I guess it'll keep my brain sharp and help my daughter in her studies down the line.
I would hope that the inclusivity is implied by the given, 0+100=100. Otherwise that's red herring information intended to send the contestant into a pitfall, and an exceptionally unsatisfying one if that were the only issue in their solution. So no, the 0 and 100 are implied included.
It's not amazing that Gauss figured this out. Gauss is in the running for the most intelligent person in human history. He discovered a great many mathematical truths. What was amazing is that Gauss discovered this when he was seven.
Germany reporting in.. we got this queststion in 12th Year with one difference: Not "left handed People" but "People" have to leave the room. So the answer was the number including the Statement" If the lefthanded didnt leave the Room, the Chance for that being 50%"
Beautifully explained! I really wish you could redo the video to cover odd numbers and how the same rule applies, even though I suspect with an odd number you can arrange all numbers leading up to it into pairs, so you won't need to add the middle number in the end. For example, if this question had 101 instead of 100.
Mean average × number of elements. In case of arithmetic progression, mean average is first + last divided by two. From 0 to 100 there are 101 elements. ((0+100)/2)*101=5050
There are 101 “number pairs” that each sums up to 100. Total sum is 101 x 100 = 10100. This is the double of the sum of the integers from to 100, meaning the sum must be half of 10100 = 10100 : 2 = 5050.
The easy way to not have to count how many 100s you have: Start with the numbers 1-100 (100 numbers, no further counting) Put a second row with the numbers in descending order (from 100 down to 1) add the rows: every result is 101 (you have 100 of these 101s) 100 x 101 (and have to divide by 2 since you added a second row) 101 x 50 = 5050
It is very simple put formula Sn=n/2[2a+(n-1)d] where a=first term,d is common difference n is number of terms Sn sum of n th terms so a=0, n= 101 d= 1, Sn= 101/2[2*0+(101-1)1] = 101/2×100 = 101×50 = 5050 ans.
there is better formula to sum up all natural numbers between lower number a and upper number b, ((a+b)/2)*(b-a+1), in this case it would be ((101)/2)*100=5050, second parenthesis represent number of elements in list so this can also be generalized to any equally spaced list of numbers where a is lower number, b is upper number and n is number of elements so we have ((a+b)/2)*n
If the question posed relies upon implying something from the “Given that” statements the answer is ambiguous. “given that” statements are just sets of info from which a “pattern/sequence of operations” can be established for the basis of the question that follows. “Whole numbers”, which the question refers to, are numbers greater than or equal to 0, the 0 + 100 = 100 is included as its part of the “pattern” that the “given that” statements are establishing The wording of the question is “Whole numbers between 0 and 100” which are 1 to 99, which does not include 0 or 100. If the 0 and 100 where to be included the wording of the question should have been “From” 0 “To” 100, Or perhaps “between and including 0 and 100” Or ‘between 0 and 100 inclusively”.
As soon as I saw the question on TV I bet my son that the show would give the wrong answer. They did. The correct answer mathematically is 4950. "Between" never includes the boundaries when used in English. (Ask any footballer trying to get a ball BETWEEN the posts whether they want to hit the boundary...)
0 to 100 has 101 number, so its 100x101 = 101.000 but because 100 is adding 2 numbers on the list (0+100, 1+99, ...), so we just need half of it 101.000/2 = 5.050
@@frankhooper7871It would matter if the question were “sum of all numbers between 100 and 200”, which would only be 101+102+…198+199. A difference of 300!
I rememmber solving this when i was like 12 My soulution is that i rememberd that usually when i play cards and i have to add numbers like 7+8+9 i can just do 3*8 and you can basicly do the sam thing with 100
Using the word between is confusing cause a lot of people like myself will say that it says "between" 0-100 therefore excluding 0 and 100. Technically anyone who answers 4950 would also be correct cause of poor wording. Except it specifically shows us 0+100 as an example thus showing us they are in fact included. So if u only heard or read the sentence without seeing the few examples showing what it's asking, then u could be forgiven for saying 4950, but the examples show the clarity.
I've given up on verbal math "problems." Words fail, there's always ambiguity, or lack of precision. Any problem presented in verbal form should cover all possibilities and eventualities, setting all the rules, thus actually containing the answer!
I think that it was gauss that solved this as a child when his teacher tried to punish him by telling gauss to add up 1 to 100. Gauss did it in a minute, I think he was 7 years old
The sum from 1 (beginning by zero has no value) to x = (x squared + x) / 2 = from 1 to 100 you have 100 squared + 100 (10.000 + 100) = 10.100 / 2 = 5.050. No need to begin and find all the pairs of hundred
@@r.h.5655 Since 0 is the additive identity, it makes no difference whether it's included or not. In any case, I'd interpret "between" as a term that excludes the two endpoints, unless it's otherwise specified.
I have a question regarding this topic. Its probably my mistake but the questions said: what is the sum(everything added up) of all the whole numbers between zero and 100. I know i am a dumbass but shouldnt you remove 100 and 0 from the questions since all numbers must be between 0 and 100
it should've been specified in the question if it was inclusive or not. The question most likely meant inclusive since that was the famous Gauss problem.
3:28 Oh my, a Christmas miracle! That said, I'm proud that I figured out the solution to this before he even mentioned gauss! I'm not useless after all!!!
The point is the child Gauss wasn’t GIVEN the the instruction ”given 1+100=101, 2+99=101,...”. He NOTICED it by himself, which you didn’t. I can therefore confirm you’re not Gauss...
I was taught that to "add up all the numbers from 0 (or 1) to N" you simply take N * (N + 1) and divide by 2. So here we have 100 * 101 = 10100, divided by 2 is 5050.
I have not watched the video yet. Hopefully this is right. Remove 50 (since there's only one). Now you have 100 numbers. That's 50 sets of two. 100x50 = 5000. Add that 50 back in. 5050.
A minus ain't squared, unless it's been snared. This means "A = -60^(1/4)" by default, means "A = -1*(60^(1/4))". The negative sign is an implied coefficient of -1, rather than an intrinsic part of the 60. Squaring both sides gives: A^2 = 60^(1/2), which simplifies to 2*sqrt(15)
the easiest way to find the toatal sum is always use the highest number in this case 100 and mulitply by next number up 101 then divide by 2 , Your welcome
@ the title literally says to include +100 in the equation. “Between” can be different things depending on whether people mean it inclusively or exclusively of the range, but in this case there’s no ambiguity between those that needs to be resolved because the ends of the range are explicitly provided in the equation.
Take the average of all the numbers from 0 to 100, which is 50. Multiply that by how many numbers there are, which is 101, and you get 5050. Why is 50 the average? Because for every pair of opposite numbers, it's the average. (0+100)/2=50 (1+99)/2=50 Etc
It's between 0 and 100 so you must exclude 0 and 100. But let's say it's including them. It's ((1+100)/2)×100. Lowest number plus highest number, divide the total by 2, multiply by the highest number. 0 doesn't play a role in the calculation.
@@Mindvirus-ly5edthey clearly mean all numbers from 0 to 100 including 0 and 100, because they literally said “0 + 100 = 100, 1 + 99 = 100, 2 + 98 = 100, etc” so you’re the one who failed
i got 2 different answers: if it’s BETWEEN 0 and 100, excluding 100, then it’s -not 4999.5 oops- 4950 (read replies) if it’s 0 to 100 inclusive, then it’s 5050
@ oh shit youre right, i did the following: 1 + 2 … + 98 + 99 = x 99 + 98 … + 2 + 1 = x if you add these two equations, you get… which wait, as im typing this im realizing a flaw, i did it not to 99 but 100, which meant adding the equations… 1 + 2 … + 99 + 100 100 + 99 … + 2 + 1 got me 101 + 101 + 101 etc, or 101*100, where right HERE at this step i incorrectly “made it exclusive” by making it times 99 instead of times 100, all equal to 2x. So “101*99 = 2x” This got me 9999 = 2x, or 4999.5 = x redoing it, if we do between 0-100 exclusive itd be 2x = 100*99 = 9900/2 = 4950, which we can also check by just taking the answer which is inclusive (5050) and subtracting 100.
Always just went with the idea of taking the number you want, in this case 100, then adding 1 to that number, then multiply the orginal number +1, with the original number divided by 2 ie (100 + 1) * (100 / 2) = 101 * 50 = 5050 For any number you want ,just add 1 to that number, then multiply that number by the original number divided by 2...any number. 10? 10 + 1 = 11, then go 11 * (10/2) = 11 * 5 = 55 It even works with uneven numbers ie 13. 13 + 1 = 14 . 13/2 = 6.5. 6.5*14 = 91... 233? (233 + 1) * (233/2) = 234 * 116.5 = 27261
Tricky 1% Question: In a room of 100, 99% are left-handed. How many left-handed people have to leave to bring that percentage down to 98%?
ua-cam.com/video/U6emQxf-cxY/v-deo.html
50, it's not 1 cuz the number of the total amount of people in the room also decreases
50, because after 50 left-handed people leave, you're left with 49 left-handed people and 1 right-handed person, and 49/50 = 98%.
@@carultch the 1 could also be ambidextrous but great explanation thank you.
50
@@bprpmathbasics can we call 97 left handed people and 3 right handed people instead?
Gauss was a legend in school..and the teacher was pissed :)
@@JossWainwright He (teacher) was pissed in the sense that he didnt want to teach that day and therefor gave the class a difficult exercise that would normaly take very long to finish. Or so thats what Ive read
I remember recently I was teaching my kids trapezoid area. It hits me that, you can use the same area formula to solve these addition sequences. Set your first term as Short-base, and last term as Long-base, the height would be number of terms (usually it's just last minus first plus one). And if it is odd/even only sequence, then half the number of terms before plus one, if it's adding every 3rd term, then 1/3 of the number plus one.
1(上底)~100(下底)共100個數字(高)
用梯形公式
(1+100)x100/2=5050
0~100(底)共101個數字(高)
用三角形公式
100x101/2=5050
都可以👍
It is easier to use 1+100=101, 2+99=101, 3+98=101........50+51=101. Therefore the sum is simply 50x101= 5050.
True, but maybe doing 50*100 + 50 instead is easier for doing the calculation in your head quickly since the gameshow is timed
Yea a kid named gauss did it in like few minutes its so not that hard.
Yeah, that’s exactly the same method gauss did
They probably start with 0 to catch the people who forget the lonely 50
@@Ninja20704not realy both are pretty much the same amount of operations with the method the commentor provided being a tiny bit less, also it follows the general formular(better/more similar) for such sums which is n*(n+1)/2 which you can also think of as adding the highst and lowest numbers together will give you allways one more than the highest, multiply this by all numbers and because you decrease the the total sums to half you get the answer. Finding a Formular for n² for example isnt this linear, still not that difficult(more annoying) if you know what to do/for any power of n or sum.
It depends on the usage of the word "between" - they should specify inclusive/exclusive in the question. I'm frequently using the BETWEEN operator in SQL, and it's always inclusive. However, prior to this, I'd always understood "between" to be exclusive.
I think of it this way: John, Ringo, George and Paul are standing in a line. How many people are standing between John and Paul?
exactly. so the answer would be 4950 then
@@shaunelliott8583Two
Exactly. Pick a number between 1 and 3 there is only one answer "2" so your comment is spot on.
yes, who ever phrased the question deserves a date with the Captain's Daughter
1 + 2 + 3 + .. + n , can be seen as one half of the number of blocks in an n x n square, if you include also the diagonal. Total number is n^2, so you subtract n for the diagonal, take half and add back in the diagonal: (n^2 - n) x 1/2 + n = 1/2 n^2 + 1/2 n.
Wow, I love how this video simplified the classic math problem. It’s amazing how understanding a simple formula can make such a big difference. Using the formula, the sum from 0 to 100 is 5050, a satisfying math trick that never gets old. Also, shoutout to SolutionInn for making concepts like these easy to practice and revisit.
first time seeing you drop the marker 3:28
I roared 😂
I probably wouldn’t have figured it out otherwise, but with the hints the show provided it was pretty easy
“Between” 0 and 100 doesn’t include the 0 or the 100. “From” 0 “To” 100 does.
What are the whole numbers “Between” 1 and 4? 2 and 3.
What are the whole numbers “From” 1 “To” 4? 1, 2, 3 and 4.
Easy: for each value of x < n/2 there is a complement n-x which when added together gives a result of n (n-x+x). This leads to an initial answer of n²/2 which may or may not need a correction depending on whether n is odd or even. If n is odd you keep the answer n²/2, if n is even you add n/2 to the initial result.
3:27
Caught in 4k.
Top ten blackpenredpen moments.
WAIT I JUST GOT TO KNOW WHAT BPRP STANDS FOR WTF
great video. I'm trying to brush up on my math after 20 years of being out of school. No real need to, but I guess it'll keep my brain sharp and help my daughter in her studies down the line.
2:00 Shouldn't it be 4950? The original says *between* 0 and 100, so I would expect 100 to be excluded from the calculation.
Maybe they didn't specify that it should be between 0 and 100 inclusive.
I would hope that the inclusivity is implied by the given, 0+100=100. Otherwise that's red herring information intended to send the contestant into a pitfall, and an exceptionally unsatisfying one if that were the only issue in their solution. So no, the 0 and 100 are implied included.
Racist. 🗿
Lolno
It's the one percent club they do that on purpose , unclear questions eliminate more people.
I used to know this formula. Thanks for reviewing it!
Math UA-camr carried me through school and now I watch it just for fun sometimes 😅❤
It's not amazing that Gauss figured this out. Gauss is in the running for the most intelligent person in human history. He discovered a great many mathematical truths.
What was amazing is that Gauss discovered this when he was seven.
Upon trying this in my head before clicking i got the whole logic right, up until the zero. Damn 0 indexing always gets me.
when calculating the number of pairs that total 100 ? Well, the rhs .. has 51 to 100 ..thats 50 pairs..
Germany reporting in.. we got this queststion in 12th Year with one difference: Not "left handed People" but "People" have to leave the room.
So the answer was the number including the Statement" If the lefthanded didnt leave the Room, the Chance for that being 50%"
Still hate that teacher...
Beautifully explained! I really wish you could redo the video to cover odd numbers and how the same rule applies, even though I suspect with an odd number you can arrange all numbers leading up to it into pairs, so you won't need to add the middle number in the end. For example, if this question had 101 instead of 100.
Mean average × number of elements. In case of arithmetic progression, mean average is first + last divided by two. From 0 to 100 there are 101 elements.
((0+100)/2)*101=5050
I did this in my head within 30 seconds without the all that crazy math. 😅
There are 101 “number pairs” that each sums up to 100. Total sum is 101 x 100 = 10100. This is the double of the sum of the integers from to 100, meaning the sum must be half of 10100 = 10100 : 2 = 5050.
The easy way to not have to count how many 100s you have:
Start with the numbers 1-100 (100 numbers, no further counting)
Put a second row with the numbers in descending order (from 100 down to 1)
add the rows: every result is 101 (you have 100 of these 101s)
100 x 101 (and have to divide by 2 since you added a second row)
101 x 50 = 5050
This is class 10th questions of Arithmetic Progression
Sum of n term = n/2 [a+ (n-1)d]
there are 99 terms in between 0 to 100
Sum=4950
It is very simple put formula Sn=n/2[2a+(n-1)d] where a=first term,d is common difference n is number of terms Sn sum of n th terms so a=0, n= 101 d= 1, Sn= 101/2[2*0+(101-1)1]
= 101/2×100
= 101×50
= 5050 ans.
there is better formula to sum up all natural numbers between lower number a and upper number b, ((a+b)/2)*(b-a+1),
in this case it would be ((101)/2)*100=5050,
second parenthesis represent number of elements in list so this can also be generalized to any equally spaced list of numbers where a is lower number, b is upper number and n is number of elements so we have ((a+b)/2)*n
I already knew the n(n+1)/2 formula.
But I didn't know about the Gauss algorithm so I thought that was clever.
N(n+1)/2 direct formula
Ok. I think I’ve just found my new favourite UA-cam channel ❤
I did it from 1 to 10... discovered that the pairs are actually 1 and 100... which adds to 101. There are 50 pairs so... 5050
If the question posed relies upon implying something from the “Given that” statements the answer is ambiguous.
“given that” statements are just sets of info from which a “pattern/sequence of operations” can be established for the basis of the question that follows. “Whole numbers”, which the question refers to, are numbers greater than or equal to 0, the 0 + 100 = 100 is included as its part of the “pattern” that the “given that” statements are establishing
The wording of the question is “Whole numbers between 0 and 100” which are 1 to 99, which does not include 0 or 100. If the 0 and 100 where to be included the wording of the question should have been “From” 0 “To” 100, Or perhaps “between and including 0 and 100” Or ‘between 0 and 100 inclusively”.
The sum of all integers from 1 to n (inclusive) is the average of n and its square.
This is the classic Gauss sum with zero added to the front. Pair 1 and 100, 2 and 99 and so on to a total of 50 pairs. The zero is just a distraction.
It's the phrasing of
Between 0 and 100 vs.
From 0 to 100
Feels like a trick question. To me 'between' doesn't include the endpoints.
The way I did it, from the thumbnail, was (100 * 101)/2. Much easier as you don’t have to worry about pairing up and the 50 on its own.
I always looked at this problem by solving a triangle.
I memorized that one through repetition decades ago 🙂
As soon as I saw the question on TV I bet my son that the show would give the wrong answer. They did. The correct answer mathematically is 4950. "Between" never includes the boundaries when used in English. (Ask any footballer trying to get a ball BETWEEN the posts whether they want to hit the boundary...)
0 to 100 has 101 number, so its 100x101 = 101.000
but because 100 is adding 2 numbers on the list (0+100, 1+99, ...), so we just need half of it 101.000/2 = 5.050
When you plug in infinity, it is -1/12 !
(I know it's wrong, the zeta function only works for s>1)
really easy 1% question with the hint too
I calculated it by multiplying 100 x average (1+100) =100 x 50.5
Dont agree it says between. 100 should not be included.
Good point. It should say “from 1 to 100”
Nor 0, of course, not that that matters.
@@frankhooper7871It would matter if the question were “sum of all numbers between 100 and 200”, which would only be 101+102+…198+199. A difference of 300!
@@frankhooper7871It does matter mate
Now, set n to infinity... s = (infinity ( infinity + 1)) / 2 , which they try to tell us is negative one-twelfth.
5050. Carl Friedrich told me, and I trust him.
I rememmber solving this when i was like 12
My soulution is that i rememberd that usually when i play cards and i have to add numbers like 7+8+9 i can just do 3*8 and you can basicly do the sam thing with 100
Using the word between is confusing cause a lot of people like myself will say that it says "between" 0-100 therefore excluding 0 and 100. Technically anyone who answers 4950 would also be correct cause of poor wording. Except it specifically shows us 0+100 as an example thus showing us they are in fact included. So if u only heard or read the sentence without seeing the few examples showing what it's asking, then u could be forgiven for saying 4950, but the examples show the clarity.
What if Regis tells ya it is multiple choice and gives ya four possibilities? So you use 50/50 and end up with - a. 5050 or b. 4950.
I've given up on verbal math "problems." Words fail, there's always ambiguity, or lack of precision. Any problem presented in verbal form should cover all possibilities and eventualities, setting all the rules, thus actually containing the answer!
I think that it was gauss that solved this as a child when his teacher tried to punish him by telling gauss to add up 1 to 100. Gauss did it in a minute, I think he was 7 years old
That was lovely 😊
(1+100)/2 × 100 = 5050. Simply, a sum of n numbers from 0 is (n + 1) /2 × n.
The first 50 numbers have a complement to get to 100, the 50 does not. 5000+50=5050
Actually it wasn't first done by Gauss there's just a story attributed to him regarding this sum. A story which may or may not be true.
You multiply the last number by the next number, then half it. 100*101=10100/2=5050.
5050/100=50.5,
5050/101=50
We do 1+100,2+99…
5000/100=50 and (50/100=0.5)
The sum from 1 (beginning by zero has no value) to x = (x squared + x) / 2 = from 1 to 100 you have 100 squared + 100 (10.000 + 100) = 10.100 / 2 = 5.050. No need to begin and find all the pairs of hundred
I was guessing 5100 but forgot 50 was by itself
Lost in translation:
Is 100 between 0 and 100?
is 0? i thought the same... define "between" :)
exacly what i was thinking
@@r.h.5655 Since 0 is the additive identity, it makes no difference whether it's included or not. In any case, I'd interpret "between" as a term that excludes the two endpoints, unless it's otherwise specified.
@@carultch thank you i agree :)
@@carultch Other versions specify that it is inclusive, this one doesn't.
Sum of arithmetic series : Numbre of terms x (1st + final term)/2
101.((100+0)/2)= 50.101=5050
Do not use a decimal point for mutiplication!
101((100 + 0)/2) = 101*50 = 5050
it's an A.P so Sn=n/2(a+l)
Sn=100/2(1+100)
Sn=50 x 101
Sn= 5050
I have a question regarding this topic. Its probably my mistake but the questions said: what is the sum(everything added up) of all the whole numbers between zero and 100. I know i am a dumbass but shouldnt you remove 100 and 0 from the questions since all numbers must be between 0 and 100
it should've been specified in the question if it was inclusive or not. The question most likely meant inclusive since that was the famous Gauss problem.
you are not a dumbass, the question writer is. between means between, period. so, 1-99
It does say between 0 and 100 (not inclusive) so excludes 0 and 100 so the answer is 4950
3:28 Oh my, a Christmas miracle!
That said, I'm proud that I figured out the solution to this before he even mentioned gauss! I'm not useless after all!!!
The point is the child Gauss wasn’t GIVEN the the instruction ”given 1+100=101, 2+99=101,...”. He NOTICED it by himself, which you didn’t. I can therefore confirm you’re not Gauss...
@ezzmagri I can also confirm I'm not gauss. I'm just proud I can finally solve something myself 🤣
Can you solve this using calculas?
Gauss!
5050 arithmetic sum formula
I was taught that to "add up all the numbers from 0 (or 1) to N" you simply take N * (N + 1) and divide by 2. So here we have 100 * 101 = 10100, divided by 2 is 5050.
I have not watched the video yet. Hopefully this is right.
Remove 50 (since there's only one). Now you have 100 numbers. That's 50 sets of two. 100x50 = 5000. Add that 50 back in.
5050.
It is 50x100 + the lone 50 left, so 5050.
I m stuck on the word "between". Is the number 100 between 0 and 100? I would say it isn't. 1 and 99 are though. So the answer is 4950.
i did it in my head in about 5secs but was 50 off as i came up with 5000.
Please help me
A=-60^(1/4) then, A^2=60^(1/2) or -60^(1/2) ??
If you write it like this:
(-60)^(1/4),
Then it's:
(-60)^(1/2).
If it's:
-1*(60)^(1/4),
Then it's:
60^(1/2)
A minus ain't squared, unless it's been snared. This means "A = -60^(1/4)" by default, means "A = -1*(60^(1/4))". The negative sign is an implied coefficient of -1, rather than an intrinsic part of the 60.
Squaring both sides gives:
A^2 = 60^(1/2), which simplifies to 2*sqrt(15)
This problem was not first solved by Gauss for sure.😂
What is the triangle of 100?
Am i the only one thinking. Why N? Why not A, C or Z! And yes, i havent got a clue what this stuff is. 👍
the easiest way to find the toatal sum is always use the highest number in this case 100 and mulitply by next number up 101 then divide by 2 , Your welcome
Just use ap series sum
(100^2 + 100) / 2 = 5,050.
100^2 is easy, it’s 10,000, and 10100/2 is just 5050. Simple math.
Minus 100, since the question is between 0 and 100 (1-99). So 4950.
@ the title literally says to include +100 in the equation. “Between” can be different things depending on whether people mean it inclusively or exclusively of the range, but in this case there’s no ambiguity between those that needs to be resolved because the ends of the range are explicitly provided in the equation.
0+1+3+3+4+5+6+.....+100
a=0, l=100 and n=101
Sn=[n(a+l)]/2
Sn=[101(0+100)]/2
Sn=[101x100]/2
Sn=101x100/2
Sn=101x50
Sn=5050
(x-1)/x = 98/100; x=50
Take the average of all the numbers from 0 to 100, which is 50. Multiply that by how many numbers there are, which is 101, and you get 5050.
Why is 50 the average? Because for every pair of opposite numbers, it's the average.
(0+100)/2=50
(1+99)/2=50
Etc
That would be wrong because average would divide by the number of elements so it would be the sum / 100. You are confusing that with median.
It's between 0 and 100 so you must exclude 0 and 100.
But let's say it's including them. It's ((1+100)/2)×100. Lowest number plus highest number, divide the total by 2, multiply by the highest number. 0 doesn't play a role in the calculation.
That's literally the equation he came up with just written differently.
101×50 = [100+1]×50 = 5000+50 = 5050
My kid cracked this when she was 8. Mind you she's half Chinese lol
Easy with a whiteboard and know math, little harder if you have 30 seconds to answer and risk loosing 10k
(n *(n+1))/2, n=100
Using Sn of AP
It's 5050
n x (n+1) / 2
I didn’t watch the video but it’s 5050, took me about 30 seconds
Fail. It's 4950. Between 0 and 100 does not include 100.
@@Mindvirus-ly5edthey clearly mean all numbers from 0 to 100 including 0 and 100, because they literally said “0 + 100 = 100, 1 + 99 = 100, 2 + 98 = 100, etc” so you’re the one who failed
Adding the 0 and 100 should not be included because neither of those numbers are **BETWEEN** 0 and 100.
50 times 100 and you have only one number 50 so 5050 nice math question.
i got 2 different answers:
if it’s BETWEEN 0 and 100, excluding 100, then it’s -not 4999.5 oops- 4950 (read replies)
if it’s 0 to 100 inclusive, then it’s 5050
How did you get a decimal for a whole number equation?
@ oh shit youre right, i did the following:
1 + 2 … + 98 + 99 = x
99 + 98 … + 2 + 1 = x
if you add these two equations, you get… which wait, as im typing this im realizing a flaw, i did it not to 99 but 100, which meant adding the equations…
1 + 2 … + 99 + 100
100 + 99 … + 2 + 1
got me 101 + 101 + 101 etc, or 101*100, where right HERE at this step i incorrectly “made it exclusive” by making it times 99 instead of times 100, all equal to 2x. So “101*99 = 2x”
This got me 9999 = 2x, or 4999.5 = x
redoing it, if we do between 0-100 exclusive itd be 2x = 100*99 = 9900/2 = 4950, which we can also check by just taking the answer which is inclusive (5050) and subtracting 100.
I thought "between" two numbers means you're not to include those two numbers mentioned in the calculation.
50×100+50=5050
100/2(1+100)=50(101)=5050
5050+0= ? 😂
Always just went with the idea of taking the number you want, in this case 100, then adding 1 to that number, then multiply the orginal number +1, with the original number divided by 2 ie
(100 + 1) * (100 / 2) = 101 * 50 = 5050
For any number you want ,just add 1 to that number, then multiply that number by the original number divided by 2...any number. 10? 10 + 1 = 11, then go 11 * (10/2) = 11 * 5 = 55
It even works with uneven numbers ie 13. 13 + 1 = 14 . 13/2 = 6.5. 6.5*14 = 91... 233? (233 + 1) * (233/2) = 234 * 116.5 = 27261
Minus 100. Does not include 100 since it is BETWEEN 0 and 100, so sum of 1-99.
50.5×100=5050
Or just simply use sum of AP
It is easy -1/12