Question

Consider the following geometric series; inf,n=0 2^(n+3) / 5^n

(a) identify value of initial term a
(b) identify value of common ratio r
(c) does the series converge or diverge and why
(d) if the series converge find sum
answer in fractions

Answer 1

2^(n+3)/5^n = 8*(2/5)^n so

a = 8
r = 2/5
S = a/(1-r) = 40/3