Question

Given the geometric series $ 15 + 5 + \frac{5}{3} + ...$

1. Explain why the series converges
2. Evaluate $ \sum_{n=1}^{\infty} 5(3^{2 - n})$

Answer 1

1. ratio =5/15 = 1/3 , -1<r<1, hence coverges

2. T1=5(3)=15

T2=5(3)^0=5  , hence the sequence in question 1,

therefore sum to infinity = a/(1-r) = 15/(1- 1/3) =  22.5