Find if the following series converges, if possible determine what it converges to

sin1nsqrtn

#1

Find if the following series converges, if possible determine what it converges to:
Sum from n=1 to infinity of [sin(1/n)]/(sqrt.n)

Answer:

Use the limit comparison test with An=(sin(1/n))/sqrt.n and Bn=1/(n*sqrt.n)
lim An/Bn = 1>0 and is convergent (p-series with p=(3/2)>1)
Therefore, is convergent too.