Answer
Diverges
Work Step by Step
Here, $ s_n=(\tan 1-\tan 0)+(\tan 2-\tan 1)+...(\tan {n+1} -\tan n)=\tan (n+1)$
We know the value of the function $\tan x$ always oscillates in between $-\infty$ and $+\infty$.
Thus, we have $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \tan (n+1)$ = Limit does not exist
Thus, the given series diverges.