Question

Find sum of the series
\[\sum_{n=1}^{\infty}\frac{1}{n^2}\]

Answer 1

I did integeate geometric series
I got this integral
\[-\int\limits_{0}^{1}\frac{\ln(1-x)}{x}\]

Answer 2

ans is (pi)^2/6

Answer 3

it is geometric series with a=1 and r=1/2 use a/(1-r) to find sum

Answer 4

http://www2.math.uu.se/~bjorklund/euler.pdf

Answer 5

Nooo

Answer 6

why u use integration to solve this

Answer 7

It's not Geometric, How could it be Geometric?

Answer 8

Awesome @Ishaan94 how do you find all this stuff

Answer 9

oh sorry.yes it is not geometric

Answer 10

Google... since 2004 Lol

Answer 11

Yeah ,,,,, I mean what do you type in the search box

Answer 12

Umm I typed 1/n^2 and then suggested searches showed up

Answer 13

Cool

Answer 14

It would take me time to digest this
thanks

Answer 15

Me too, thanks for posting the question.

Answer 16

This can be helpful too http://en.wikipedia.org/wiki/Basel_problem

Answer 17

We were discussing this thing yesterday (Me, Turing and Badref)

Answer 18

It took Euler 6 years to get the rigorous proof. :-O

Answer 19

Btw Robin chapman has this lovely collection of proofs on his homepage : http://empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf

Answer 20

And here is the url of the epic discussion on M.SE : http://math.stackexchange.com/questions/8337/

Answer 21

@Ishaan94: And this is how Euler did it http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2002%20Estimating%20the%20Basel%20Problem.pdf

Answer 22

Wow

Answer 23

:-)