Series converges or diverges

Question

∞
∑ (5)/(n√n)
n=1

Answer 1

∞
∑ (5)/(n√n)
n=1

can be written as

∞
∑ 5/n^3/2
n=1

This is a p series which is convergent if p > 1. Since in this case p = 3/2 > 1, then the above series converges.