I cant find an example of this series, could I get some help please?

Question

1. Use an appropriate test to determine if the given series converges. You must give a well written reason for your conclusion.
2. 

Answer 1

Use the Direct comparison test where a_k =10cos²k/(k³+3k+8)^1/2 and b_k=10/k^3/2 thus b_k>a_k>0 and b_k converges by P test where P=3/2>1. Thus a_k converges