The answer is 16, i am just not sure how to arrive at that answer.

Step-by-step explanation:

∑ (4ⁿ⁺¹ / 5ⁿ)

Rewrite 4ⁿ⁺¹ as 4 (4ⁿ).

∑ 4 (4ⁿ / 5ⁿ)

∑ 4 (4/5)ⁿ

This is a geometric series.  The sum of an infinite geometric series is:

S = a / (1 −r)

where a is the first term and r is the common ratio.

Here, the first term is 16/5 (because n starts at 1), and the common ratio is 4/5.

S = 16/5 / (1−4/5)

S = 16/5 / (1/5)

S = 16