If $\displaystyle
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 $\displaystyle \frac{dy}{dx} = \frac{1}{(x+n)^2 + 1} - \frac{1}{x^2+1}$
If $\displaystyle
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 $\displaystyle \frac{dy}{dx} = \frac{1}{(x+n)^2 + 1} - \frac{1}{x^2+1}$