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Math Help - Divergence/Convergence Conflicting Tests?

  1. #1
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    Divergence/Convergence Conflicting Tests?

    Determine whether the series is convergent or divergent:

    The sum from n=1 to infinity of the series 1/(5n+2).

    I used the divergence test -- lim(n->inf) of 1/(5n+2) -> infinity, therefore, not divergent.

    But if I integrate,

    The integral from 1 to inf of 1/(5x+2) dx ; lim(t->inf) of the integral of 1 to t of 1/(5x+2) dx, use u substitution, etcetera, to come out with

    (1/5) lim(t->inf) of ln|5t+2| - ln|7|, which is of course infinity.

    ? Help

    Am I just not understanding something here?
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  2. #2
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    Re: Divergence/Convergence Conflicting Tests?

    Quote Originally Posted by Stephan View Post
    Determine whether the series is convergent or divergent:
    The sum from n=1 to infinity of the series 1/(5n+2).

    This problem is ideal for the Limit Comparison Test. Use \frac{1}{n} for comparison.

    Or note that \frac{1}{5n+2}>\frac{1}{10n}=\frac{1}{10}\frac{1}{  n}: basic comparison .
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