using direct comparison test, determine if the series converges or diverges.

Question

Answer 1

We will choose for comparison the p-series ∑_n=1^∞ 1/n² which is convergent since p = 2 and 2 > 1.

0 ≤ sin²n ≤ 1 for all n ∈ Ν , and n² + 5 > n² for all n ∈ N.

So, since each term in the given series is smaller than the corresponding term in the p-series, the series converges.