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chris

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

  • 2 years ago
  • 2 years ago

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  1. PreMedExpert
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    I would like to know how tosolve that as well.

    • 2 years ago
  2. siddharth
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    Isn't this the Euler Series?

    • 2 years ago
  3. shadowfiend
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    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.

    • 2 years ago
  4. imranmeah91
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    By integral test, it does converge

    • 2 years ago
  5. siddharth
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    Oh right, this is the basel problem that Euler solved, which made him famous

    • 2 years ago
  6. shadowfiend
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    Fair point, it does. Good catch siddharth!

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

    • 2 years ago
  8. turnand
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    The answer is \[\pi ^{2}/6\]

    • 2 years ago
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