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  1. MHB Apprentice

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    #1
    Can anyone help with this problem. I've tried integral test but seems to be too complicated.

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    #2
    Quote Originally Posted by Linus12351 View Post
    Can anyone help with this problem. I've tried integral test but seems to be too complicated.
    Have you tried looking at $ \displaystyle \lim_{n \to \infty} \dfrac{a_{n + 1}}{a_n}$?

    -Dan

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    #3
    Quote Originally Posted by Linus12351 View Post
    Can anyone help with this problem. I've tried integral test but seems to be too complicated.
    Easy,

    $\displaystyle 0 \leq \sum{\frac{1}{5^{n-1} + 1}} < \sum{\frac{1}{5^{n-1}}} = \sum{ \left( \frac{1}{5} \right) ^{n-1} }$

    Since your positive term series is less than a convergent geometric series, your series converges by comparison.

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