Question

what is the sum of 1/n^2 from 0 to infinity?

Answer 1

I would like to know how tosolve that as well.

Answer 2

Isn't this the Euler Series?

Answer 3

Yeah, I think this sum doesn't converge, but I'm not sure. The ratio test and root test seem to be inconclusive in this case.

Answer 4

By integral test, it does converge

Answer 5

Oh right, this is the basel problem that Euler solved, which made him famous

Answer 6

Fair point, it does. Good catch siddharth!

Answer 7

ah sorry, i should have said 1 to infinity :-). 1/0^2 can obviously not converge

Answer 8

The answer is \[\pi ^{2}/6\]