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Math Help - Finding the sum, verify my answer please.

  1. #1
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    Finding the sum, verify my answer please.

    Hello,

    Can someone please verify my answer?

    Here's what I got: 8/2e-10

    Thanks,
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  2. #2
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    Re: Finding the sum, verify my answer please.

    Quote Originally Posted by l flipboi l View Post
    Hello,

    Can someone please verify my answer?

    Here's what I got: 8/2e-10

    Thanks,
    \displaystyle \begin{align*} \sum_{n = 1}^{\infty}\left[\frac{5}{e^n} + \frac{3}{n(n + 1)}\right] &= 5\sum_{n = 1}^{\infty}\left(\frac{1}{e}\right)^n + 3\sum_{n = 1}^{\infty}\left(\frac{1}{n} - \frac{1}{n + 1}\right) \\ &= 5\left(\frac{\frac{1}{e}}{1 - \frac{1}{e}}\right) + 3\lim_{n \to \infty}\left(1 - \frac{1}{n + 1}\right) \\ &= \frac{5}{e - 1} + 3 \\ &= \frac{5}{e-1} + \frac{3(e-1)}{e - 1} \\ &= \frac{3e + 2}{e - 1} \end{align*}
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