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Math Help - Weierstrass M-test

  1. #1
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    Weierstrass M-test

    So thanks to tph we know that \sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k} converges on (-\sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}}).

    To use the Weierstrass M-test, how do we find a bound for that sum.

    Thanks
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  2. #2
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    Quote Originally Posted by tbyou87 View Post
    So thanks to tph we know that \sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k} converges on (-\sqrt{\frac{3}{2}}, \sqrt{\frac{3}{2}}).

    To use the Weierstrass M-test, how do we find a bound for that sum.

    Thanks
    What are you trying to show? We can show that if 0<r<R where R=\sqrt{3/2} then \sum_{k=0}^{\infty}\frac{k2^k}{3^k}x^{2k} converges uniformly on [-r,r] by choosing M_k = \frac{k2^k}{3^k}r^{2k}.
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