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Math Help - Test Convergence

  1. #1
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    Test Convergence

    Test the convergence of the series
    \frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{  x^6}{5\sqrt{4}}+...
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  2. #2
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    Quote Originally Posted by varunnayudu View Post
    Test the convergence of the series
    \frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{  x^6}{5\sqrt{4}}+...
    a_n = \frac{x^{2n}}{(n+2)\sqrt{n+1}}.

    Now apply the ratio test to get the radius of convergence. To check convergence at the endpoints I'd suggest using the comparison test.
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  3. #3
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    This is an even function --> It's enough on [0, inf] to test.

    divide this interval to [0, 1), [1], (1, inf] and test separatting.
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