## Thomas' Calculus 13th Edition

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.