Divergence and convergence

Question

Determine whether or not the following series converge or not

a) ∑_n=0^∞ (-1)^n/(3n+3)

b) ∑_n=1^∞ 2^n/(n+3)!

c) ∑_n=1^∞ (16/n^3)^(1/4)

Answer 1

a) ∑_n=0^∞ (-1)^n/(3n+3) converges conditionally by the alternating series test

b) ∑_n=1^∞ 2^n/(n+3)! converges by the ratio test.

c) ∑_n=1^∞ (16/n^3)^(1/4) diverges by the p-series test