If the following series converges, compute its sum.

Question

 If the following series converges, compute its sum. Otherwise, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, and DIV otherwise.

∑n=1to inf (3+5^n)/5^n

Answer 1

(3 + 5ⁿ) / 5ⁿ

(3 / 5ⁿ) + (5ⁿ / 5ⁿ)

(3 / 5ⁿ) + 1

While the first term converges to 0 the summation of the second term is an unlimited number of 1's.

i.e.: [3/5 + 1] + [3/25 + 1] + [3/125 + 1], [3/625 + 1].......

Diverges

Answer 2

Since the nth term converges to 1, this series cannot converge.