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Math Help - Convergence question

  1. #1
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    Convergence question

    Use the integral test to determine whether the series converges:  \sum^{\infty}_{n=1} \frac{1}{(2n+1)^3}

    I was thinking instead of using the integral test I just make (2n+1) = x which becomes  \sum^{\infty}_{n=1} \frac{1}{(x)^3} which is a p-series and is clearly convergent. Would that be a valid assumption?
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  2. #2
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    Quote Originally Posted by lllll View Post
    Use the integral test to determine whether the series converges:  \sum^{\infty}_{n=1} \frac{1}{(2n+1)^3}

    I was thinking instead of using the integral test I just make (2n+1) = x which becomes  \sum^{\infty}_{n=1} \frac{1}{(x)^3} which is a p-series and is clearly convergent. Would that be a valid assumption?
    Do not use integral test, 0 \leq \frac{1}{(2n+1)^3} \leq \frac{1}{n^3}.
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