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Math Help - Please give me a hint on how to solve this?

  1. #1
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    Please give me a hint on how to solve this?

    If <br />
y = tan^{-1}\frac{1}{x^2+x+1} + tan^{-1}\frac{1}{x^2+3x+3} + tan^{-1} \frac{1}{x^2+5x+7} +.....<br />
to n terms. Then prove that \frac{dy}{dx} = \frac{1}{(x+n)^2 + 1} - \frac{1}{x^2+1}
    Last edited by mr fantastic; September 25th 2009 at 03:32 AM. Reason: Fixed the -1 superscripts with ^{-1}
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  2. #2
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    Quote Originally Posted by rajeshj.lnt View Post
    If <br />
y = tan^{-1}\frac{1}{x^2+x+1} + tan^{-1}\frac{1}{x^2+3x+3} + tan^{-1} \frac{1}{x^2+5x+7} +.....<br />
to n terms. Then prove that \frac{dy}{dx} = \frac{1}{(x+n)^2 + 1} - \frac{1}{x^2+1}
    My hint would be by induction noting that the nth term in y is

    \tan^{-1}\left( \frac{1}{x^2 +(2n-1)x + n^2-n+1}\right)
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