How do you do this question?

0

Convergent

Step-by-step explanation:

aₙ = 2ⁿ / n!

aₙ₊₁ = 2ⁿ⁺¹ / (n+1)!

lim(n→∞)│(2ⁿ⁺¹ / (n+1)!) / (2ⁿ / n!)│

lim(n→∞)│(2ⁿ⁺¹ / (n+1)!) × (n! / 2ⁿ)│

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

Notice that (n+1)! = (n+1) n!.  So this reduces to:

lim(n→∞)│2 × 1 / (n+1)│

0

The limit is less than 1, so the series is absolutely convergent.

x+14

step-by-step explanation: