Olympiad | Which is Larger? | A Nice Exponent and Factorial Math Simplification |
Вставка
- Опубліковано 9 лют 2025
- Math with fun.
Hello My Dear Family
I hope you all are well
.
.
.
France Math Olympiad | Calculator Not Allowed! | You should know this trick!
find the value of x exponents and powers
the math scholar
factoring exponential equations
solving exponential equations
equations with rational exponents
values of teaching mathematics
Exponential Equation
exponents and powers class 8 olympiad
exponents and powers olympiad questions
exponents and powers class 7 olympiad
kulkarni sir maths classes
basic mathematics for entrance exam
math scholar
the math
the math scholar
the scholar
scholars
themathscholar23
themathscholar
A Nice Algebra Math Simplification #mathmatics #Olympiad
A Nice Algebra Problem | Math Olympiad | Find the value of x
A Nice Algebra Problem | Can you solve this ? | Math Olympiad | X=?
One of The Hardest International Maths Olympiad Problem
International Mathematical Olympiad Problem
One of the HARDEST International Math Olympiad Question
How To Solve A Homemade Exponential Equation
Math Olympiad | A Nice Algebra Problem | How to solve for X in this Problem ?
Math Olympiad Problem, you should learn this trick!
Math Olympiad Problem For Geniuses | Is This Real?
Nice Square Root Math Simplification
themath
themaths
mathscholar
tehscholar
#themathscholar
#themathsholar23
Your quarries
DECIFRE o cÓDIGO LÓGICO
Essa é fácil mas a maioria não consegue |
Raciocinio lógico !
15÷3(3+3(3+3))=?
Nice Algebra Math Simplification Find Value Of X
👇
Nice Square Roots Math Simplification | Find Value Of X
France | Can you solve this? | Math Olympiad | X=? & y=?
France | Can you solve this? | Math Olympiad
China | Can you solve this? | Math Olympiad |X=?
Japanese Math Olympiad | Calculators Not allowed | You should know this trick !
A Nice Algebra Problem |X=?
Olympiad Algebra
Method of Functional Equations
Japanese | Can You Solve this? Math Olympiad | a=? , b=?
A Nice Algebra Problem | How to solve for X and Y in this Problem
Olympiad Algebra
Solving A Quartic Equations
.
olympiad prepare
international olympiad maths
olympiad mathematics
international olympiads
international maths olympiad
olympiad
international mathematics olympiad
mathematics
math olympiad
international math olympiad 2010
international math olympiad
math olympiad problem
math olympiad preparation
american math olympiad question
math olympiad questions
math olympiad question
math olympiad problem
olympiad mathematics
math olympiad
math olympiad training
france maths olympiad
math olympiad problems
math olympiad preparation
math olympiad questions
math olympiad algebra problem
maths olympiad
olympiad, mathematical olympiad
france math olympiad question
olympiad math problems
france maths olympiad preparation
olympiad math
maths trick
गणित
अंक शास्त्र
ریاضی गणित का होमवर्क
गणित की कक्षा
गणित के प्रश्न
Marcemetica
math olympiad algebra
france math olympiad questions
high school math
France | Can You Solve this ? Math Olympiad
can you solve this complex problem?
can you solve this logic puzzle?
can you solve this olympiad question?
olympiad
maths olympiad
olympiad mathematics
math olympiad
math olympiad question
math olympiad questions
mathematical olympiad
math olympiad training
math olympiad preparation
math olympiad problem
math solver sir
olympiad math
math olympiad algebra problem
math olympiad problems
olympiad math problems
maths maam
france maths olympiad
Luxembourg- Math Olympiad Questions
Mamta maam
thailand junior maths olympiad problem
olympiad math problems mamta
beautiful algebra problem
viral math problem, math olympiad problem
Math Olynmpiad Question | Equation Solving| You should know this trick!!
Japanese -A Nice Math Olympiad Problem
Jarman - Math Olympiad Problem | You should know this trick!!
Viral Math Olympiad Problem | How to solve
Algebra - Nice Math Olympiad Problem #maths
US Math Olympiad problem #maths
Nice Exponent Math Simplification | Find the value of X??
Math Olympiad Question | Nice Algebraic Equations
math olympiad problems ! viral math problems
Brazil Maths Olympiad Question #maths
Math Olympiad Question | Algebra
A Nice Chinese Olympiad Exponential Problem
A Nice Math Olympiad Exponential Problem
#maths
#matholympaid
#algebra
#mathematics
#lklogic
#mathbooster
#learncommunolizer
#premath
#sybermath
#mathwindow
#math #mathematics #themath #themathscholar #mathscholar #themathscholar23 #olympiadmath #sat #gre #lklogic #grequant #matholympiad
#math #mathstudent #mathproblems #mathteacher #mathematics #mathisfun #ssc #ssccgl #sscchsl #sscgk #upsc #upscaspirants #upscpreparation #upscnotes #upscmains
Amazing explanation!
I solved the problem looking at the value of 99! which can be seen as the following product (1x99)(2x98)(3x97) … (48x52)(49x51)(50) each element is something like (50-k)(50+k) with k=1,2 …49 and it is easy to see that (50-k)(50+k)=50^2-k^2 < 50^2 for each k, so 99! < 50^99.
One might ask "Okay we're grouping the terms in these pairs, and the first couple are greater than 1 and the next to last one is greater than 1, but how do we know one of the ones we didn't calculate is greater than 1?"
It comes down to why they are paired as they are. For this problem, the denominator for all of the terms contains numbers that are the same distance from 50 (in opposite directions). So (50^2)/ (99*1) could be written as (50^2)/[(50+49)(50-49)]. You could pick any pair we didn't see: 70/30, 55/45, 63/37, etc, you're basically adding x to one number and subtracting x from another. So this leads to:
(50^2)/[(50+x)(50-x)]
(50^2)/[(50^2)-50x+50x-(x^2)]
(50^2)/[(50^2)-(x^2)]
Since in the denominator we're always taking something away from 50 squared, then 50 squared in the numerator will always be bigger for all x between 49 and 1.
Take the natural log of both terms.
ln(50^99=99*ln(50)=387.29...
ln(n!)=n*ln(n)-n+O[ln(n)]; ln(99!)=99*ln(99)-99=356±O(4.6)
So 50^99>99!
1×99 × 2×98 ×...
50×50 × 50×50 ×...
The second one is clearly greater, because the biggest rectangle of a given perimeter is the square.
I had not seen this … my idea was exactly the same
You could have shown
51*49=(50+1)(50-1)=50^2-1
Er, the solution is obvious just with common-sense mathematics....