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Thread: Integral Homework Question

  1. #1
    Apr 2013

    Integral Homework Question

    Good Evening Everyone, recently in my first year single variable Calculus class we started learning integrals. I have been working on a homework problem that I believe to have solved as my prof said the answer was 0. Proof is posted and I would just like some clarification with the format of my answer (ie. is right). Thank you for your help.
    The question is:
    Integral Homework Question-screen-shot-2013-11-19-6.16.57-pm.png
    My answer is:
    Integral Homework Question-screen-shot-2013-11-19-6.30.47-pm.png
    Last edited by digidako; Nov 19th 2013 at 02:40 PM.
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  2. #2
    MHF Contributor

    Apr 2005

    Re: Integral Homework Question

    Your very first step is wrong. You have, to start,
    $\displaystyle \frac{3}{n}\left[\sum_{n=1}^\infty \left(\frac{3i^2}\right){n^2}- 2\left(\frac{3i}{n}\right)\right]$
    and the next line is
    $\displaystyle \frac{3}{n}\left[\frac{1}{n^2}\sum_{n=1}^\infty 3i^2- 6i\right]$
    You have factored $\displaystyle 1/n^2$ out of both first and second terms in the sum, but there was no "$\displaystyle 1/n^2$" in the second term.

    Instead, divide it into two sums: $\displaystyle \frac{3}{n}\left[\frac{1}{n^2}\sum_{n=1}^\infty 3i^2- \frac{1}{n}\sum_{n=1}^\infty 6i\right]$

    That is the same as $\displaystyle \frac{3}{n}\left[\frac{3}{n^2}\sum_{n=1}^\infty i^2- \frac{6}{n}\sum_{n=1}^\infty i\right]$
    You should know formulas for the sums $\displaystyle i$ and $\displaystyle i^2$
    Last edited by HallsofIvy; Nov 19th 2013 at 05:14 PM.
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