determine whether it diverges or con-verges. Make sure to state what test you are using. ∑∞k=1, 2^n/3n!

Answer 1

You might apply the ratio test: a_n+1 / a_n = (2ⁿ⁺¹ / 3(n+1)!) / (2ⁿ / 3n!) = (2ⁿ⁺¹ / 3(n+1)!) · (3n! / 2ⁿ) = 2 / (n+1)

Thus, lim_n→∞ a_n+1 / a_n = 0, and the series converges by the ratio test.