## University Calculus: Early Transcendentals (3rd Edition)

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.