Please follow the each instruction (Clear and step by step work is needed for each problem).

1. Use the Direct Comparison Test to determine whether or not the series converges. Justify your conclusion.

n=04nsin2(n)+3

2. Use the Integral Test to determine if the following series converges or diverges. You may assume the conditions of the Integral test are satisfied. Just compute the integral and state whether or not the result implies convergence.

n=1(n2+1)2n