Question

determine whethere the sequence a(n)=nsinn/n^3 converges or diverges. Explain why it does or does not converge. If it converges find the limit.

Sin(n) is always between -1 and 1. So, you have:

-1/n^2 < a(n) < 1/n^2

Both the lower bound and the upper bound converge to zero, so the sequence converges to zero.