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Math Help - Series converge?

  1. #1
    Member Pranas's Avatar
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    Series converge?

    Hints would be greatly appreciated.

    Does the series converge or diverge?


    For what k does the series converge?


    Thanks in advance!
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  2. #2
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    Quote Originally Posted by Pranas View Post
    Hints would be greatly appreciated.

    Does the series converge or diverge?


    For what k does the series converge?


    Thanks in advance!


    sin^3(x) = sin(x)(1 - cos^2(x)) = sin(x) - sin(x)co^2(x) , so that the integral equals -cos(x) + (1/2)cos^3(x) between 0 and pi/n...take it from here

    Tonio
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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Pranas View Post
    Hints would be greatly appreciated.

    Does the series converge or diverge?


    For what k does the series converge?


    Thanks in advance!
    With a little effort You find that is...

    (1)

    ... so that You have to test the convergence of the series...

    (2)

    (3)

    For the (2) You can use the expansion...

    (4)

    ... and obtain...



    (5)

    It is well known that for k>0 so that the series (2) converges. The test for the series (3) is left to You...

    Kind regards

    \chi \sigma
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