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chris

  • 3 years ago

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

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  1. PreMedExpert
    • 3 years ago
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    I would like to know how tosolve that as well.

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

  3. shadowfiend
    • 3 years ago
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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.

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

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

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

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

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

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