Question

Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div . ∑n=1[infinity]arctan(15n)

Answer 1

This series diverges, since

$\displaystyle\lim_{n\to\infty}\arctan(15n)=\frac\pi2\neq0$

(that the summand approaches 0 is a necessary condition for convergence, but not sufficient for it)