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

break the problem into two pieces. The first being 274k/k2^k=274/2^k=274*(1/2)^k is a geometric series with r=1/2 <1 thus it converges

The second piece is 2023/k2^k . Let that be a_k. Let b^k=2023(1/2)^k. Use the Direct comparison test to show a_k converges as it is less than b_k and positive and b_k converges.