Would it be pissble for someone to help me fully breakdown t

Would it be pissble for someone to help me fully breakdown this series question? Thank you

Solution

lim n->infinity (-1)^n*5n/(3n^2 - 2n +1) = 0 hence the series converges lim n->infinity (-1)^n*sin(n)/n^2 = 0 hence the series converges lim n->infinity cos(1/n!) = 1 hence the series diverges