Question

Determine the convergence or divergence of the series. Find the limit. Indicate the test that was used and justify your answer by showing evidence why the test succeeds or fails.

Sigma (lower index n = 1; upper index infinity) 12/[n(n+3)]

Answer 1

we know that sum 1/n^2 = pi/6

Since n(n+3) > n^2, it also converges