Question

How do you do this question?

Answer 1

Divergent

Explanation:

an = 3 sin(2/n)

Choose bn = 3 (2/n).

Using Limit Comparison Test:

lim(n→∞) an / bn

= lim(n→∞) [3 sin(2/n)] / [3 (2/n)]

= lim(n→∞) [sin(2/n)] / (2/n)

= 1

The limit is greater than 0, and bn diverges, so an also diverges.