# Thread: Please give me a hint on how to solve this?

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

If $
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} +.....
$
to n terms. Then prove that $\frac{dy}{dx} = \frac{1}{(x+n)^2 + 1} - \frac{1}{x^2+1}$

2. Originally Posted by rajeshj.lnt
If $
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} +.....
$
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

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