Find the Sum of this Infinite Series | No Calculators Allowed! | Train Your Brain

#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam

[makingoftheseventeenthice]

I have seen almost all your videos these days, really a good source

[Szynkaa]

Let's consider series from n=1 to inf (x^(2n+1)/2^(2n-1)). This is geometric series with sum equal to 2x^3/(4-x^2). Now take derivative both sides and put x=1. You will get that the sum you are looking for is (2x^3/(4-x^2))' at x=1 which is 22/9

[sandanadurair]

this problem can be divided into infinite number of G-series with different first terms and 1/4 as common ratio.

S1 = 3 = 3[(4/3)(1/2)] = 2 using Sg = a0/(1-r)

S2 = = 2[(4/3)(1/8)]
S3 = = 2[(4/3)(1/32)]
S4 = = 2[(4/3)(1/128)]
...
....

Let S = = 2[(4/3) = 2[(4/3){(4/3)(1/8)}] = 4/9

Total sum of given G-series T = S1 + S = 2 + 4/9 = 22/9

1/2 + 1/2 + 1/2
1/8 + 1/8 + 1/8 + 1/8 + 1/8
1/32 + 1/32 +1/32 + 1/32 + 1/32 + 1/32 + 1/32
1/128 + 1/128 +1/128 + 1/128 + 1/128 + 1/128 + 1/128 + 1/128 + 1/128
1/512 + 1/512 +1/512 + 1/512 + 1/512 + 1/512 + 1/512 + 1/512 + 1/512 +1/512 +1/512
....
....
....

[arabideas]

You're an inspiring person for People
These problems burn the passion inside me
Love math

[HappyFamilyOnline]

Amazing work 👍👍
Thank you so much sir😊😊

[sadeekmuhammadryan]

The trick is really a good one. Thank You! ❤️💯

[phanimaheswara]

Exactly sir I've got this doubt only but today it's clear thank you sir.

[srividhyamoorthy]

Thanks sir for a lot of videos hope to see the glorious face of yours in a future video

[iZAPMath]

PreMath, I miss my days in school and we didn't use calculators either! You are the best, sir!

[adelinwitty]

absolutely.i like to watch at you videos

[leok]

Respected Sir, your videos are very informative. 👍 We get a lot to learn. 😇
I recently got to know about RAMANUJAN'S SUMMATION paradox, where 1+2+3+4+5+... = -1/12.
It would be helpful, if you could share yor views on it. 😇 Advance thanks. 👍

[susennath]

Lovely.

Again nostralgic

At my class eleven I had done this sum in book Higher Algebra wrote by Hall and Kight

[furzaanullah]

Very nicely done. I am back 🔙. I will comment daily. Keep

[shashwatvats]

Nice question, today I learn again one thing

[gumnaam]

This question is from what chapter and what class ??

[petekutheis]

That one was really doable "in-head"

[sokoudamm]

I don't understand about
+....=?
Why finaly don't see?

[suvamkumarsahoo]

Sir please check the previous video on quadrilateral. I commented there by solving it by another method please check it and comment on that is it correct or not

[wackojacko]

Non-terminating decimal...unlike pi non-terminating non repeating decimal. Strange things happening out there in infinity....maintain your point of conciousness and kick these paradoxes outtta the way! I don't know, I'm nuts..., but I love ya.

[kvichuiyer]

Good! Nicely explained . Age 90 student!