Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.

Question

sum from 1 to infinity of (5^n+4^n)/20^n
It is convergent, but I do not know how to find the sum.

Answer 1

20^n = 5^n * 4^n
so, you have

5^n/20^n + 4^n/20^n = 1/4^n + 1/5^n

both of which converge