1/1^2 + 1/2^2 + 1/3^2 +.........upto infinity = how much?

Question

The question is related to +2 level maths. Let me know some maths related sites.

Answer 1

Dear friend,

You're proposing us the famous Basel Problem, solved by Leonhard Euler in 1735. You should try Euler's approach to the problem, you can see it in the following link:

http://en.wikipedia.org/wiki/Basel_problem#Euler_attacks_the_problem

Hope I've helped on something, and wish you a nice day!

Answer 2

The answer is pi^2 /6. I don't know of an easy way to see this. Usually is is proven using the Fourier series of the function f(x)=x-pi.
When you figure out the coefficients and apply the Placherel theorem, you can derive the sum.

This number is also called zeta(2). In general zeta(n) is the sum of
1/1^n +1/2^n +1/3^n+...

There are explicit formulas for zeta values at even integers. It is known that zeta(3) is irrational, but very little else is known about zeta at odd integers.

Answer 3

The answer is (pi^2)/6.

This is a very famous problem solved by Euler. For this, try the following site; just go and search it.

Answer 4

I think u need to use binomial theorem in this question. Try it out with negative powers of polynomial as they expand into infinite series and then try integration or differentiation.

Try this link
http://mathworld.wolfram.com/topics/Algebra.html

Answer 5

Unless you define the number to stop at, the answer is an infinite number.

Answer 6

(pi^2)/6.