Use the ratio test to show that the series is convergent.

Step-by-step explanation:

∑ 2ⁿ / (n+1)!

Applying ratio test:

lim(n→∞) [2ⁿ⁺¹ / (n+2)!] / [2ⁿ / (n+1)!]

lim(n→∞) [2ⁿ⁺¹ / (n+2)!] × [(n+1)! / 2ⁿ]

lim(n→∞) [2 / (n+2)]

0

Since the limit is less than 1, the series converges.