Differentiate, sub x=1, Doesn't EVERYONE know that the sum of the first 100 natural numbers is 5050? It's a classic story. And I refuse to believe that MIT would include such a simple thing. I did it in 10 seconds in my head
Yes I know it's trivial... But I found it and it is from the Mit-Harvard mathematics competition from 2008... I know it is trivial but sometimes making videos aimed at students who are beginning to learn calculus helps your channel and especially them... They could find it cool (because it is) and be motivated to learn the topic... Don't worry I'm going to make videos about more advanced questions but it's always good to make videos for everyone!!!😉🤗 BTW, I'm 17 years old so you probably understand more maths than I do but I always try to give my best to study and share my passion for maths on UA-cam!!!😉
I just tried to take derivetive for first three and plug x=1. Now I see that it is just arithmetic sequence from high school (1+2+3+...+100) so i use equation to calculate sum of that sequence ((a_1+a_n)n/2) and we get 5050 :)). Good stuff bro I like watching your videos :))
Do you like videos about math tournaments questions???🤩🤩🤩 Let me know!!!⬇️
There's absolutely no way such an easy question is from such a tournament. Unless maybe it's the very first eady one.
Yes I think so.... The tournaments have amazingly difficult questions... I'm going to make a video about one of those more difficult ones!!!😉
Alternate solution: Define g(x) = (1-x^101)/(1-x). One can check that f'(1) = lim_{x \to 1} g'(x), where the RHS equals 101*100/2 by L'Hopital's rule.
Wow cool!!!🤩🤩🤩 Thank you so much!!!🤗🤗🤗
Differentiate, sub x=1, Doesn't EVERYONE know that the sum of the first 100 natural numbers is 5050? It's a classic story.
And I refuse to believe that MIT would include such a simple thing. I did it in 10 seconds in my head
Yes I know it's trivial... But I found it and it is from the Mit-Harvard mathematics competition from 2008... I know it is trivial but sometimes making videos aimed at students who are beginning to learn calculus helps your channel and especially them... They could find it cool (because it is) and be motivated to learn the topic... Don't worry I'm going to make videos about more advanced questions but it's always good to make videos for everyone!!!😉🤗 BTW, I'm 17 years old so you probably understand more maths than I do but I always try to give my best to study and share my passion for maths on UA-cam!!!😉
Btw thanks for watching my videos!!!😉🤗
I just tried to take derivetive for first three and plug x=1. Now I see that it is just arithmetic sequence from high school (1+2+3+...+100) so i use equation to calculate sum of that sequence ((a_1+a_n)n/2) and we get 5050 :)).
Good stuff bro I like watching your videos :))
Thank you so much!!! Yes you're right!!!😉🤗
No
What do you mean by no you don't like this problem?😅😉
5050
Yes you're right!!!🤩😉