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Math Help - Comparison Theorem

  1. #1
    Member FalconPUNCH!'s Avatar
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    Comparison Theorem

    1. \sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}}

    2. \sum_{n = 1}^{\infty} \frac{n^{2} - 5n}{n^{3} + n + 1}

    I don't really understand how to use the comparison theorem.
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    1. \sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}}
    Idea: \left(1 - \frac1{n}\right) < 1 \Rightarrow \sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}} < \sum_{n = 1}^{\infty} \frac1{4^{n}}
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