Question

find the sum of the series from 0 to infinity of (3^n+5^n)/8^n

Answer 1

= sum of two series: (3^n)/(8^n)+ (5^n)/(8^n)
because each of geometric series is convergent (3/8 and 5/8 are <1) use formula for geo series:
= 1/(1-3/8) + 1/(1-5/8)= 8/5 + 8/3 = 64/15

Answer 2

Thanks!