TITLE: Is there a way to write this expression differently: $\arctan 1/(1+n+n^2)$?
QUESTION [6 upvotes]: $$ \arctan\left(\frac{1}{1+n+n^2}\right)$$
My professor wrote this as
$$\arctan(n+1) - \arctan(n)$$ 
I don't understand how this expression is right?

REPLY [10 votes]: See this diagram (drawn for $n=3$, but the principle is general):

The red line has slope $\dfrac{1}{1+n+n^2}$ and makes an angle of $\tan^{-1}(n+1)-\tan^{-1}(n)$ with the horizontal axis.