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