chris
  • chris
what is the sum of 1/n^2 from 0 to infinity?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I would like to know how tosolve that as well.
siddharth
  • siddharth
Isn't this the Euler Series?
shadowfiend
  • shadowfiend
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.

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anonymous
  • anonymous
By integral test, it does converge
siddharth
  • siddharth
Oh right, this is the basel problem that Euler solved, which made him famous
shadowfiend
  • shadowfiend
Fair point, it does. Good catch siddharth!
chris
  • chris
ah sorry, i should have said 1 to infinity :-). 1/0^2 can obviously not converge
anonymous
  • anonymous
The answer is \[\pi ^{2}/6\]

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