Answer
Diverges; Limit does not exist
Work Step by Step
The nth partial sums are: $ s_n=(\tan 1-\tan 0)+(\tan 2-\tan 1)+...(\tan {n+1} -\tan n)=\tan (n+1)$
Since, the value for $\tan x$ is always oscillates in between $-\infty$ and $+\infty$.
Then after applying limits , we have $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \tan (n+1)$
This implies that Limit does not exist
Now, the given series diverges.
