Mathematics

Problem

Two infinite geometric series are given below. Series

A

: first term

12

and common ratio

\frac{1}{4}

Series

B

: first term

9

and common ratio

\frac{2}{5}

Respond to the tasks that follow. a. (i) Find the sum to infinity of Series

A

and of Series

B

. b. (ii) Calculate the ratio

\dfrac{S_A}{S_B}

, where

S_A

and

S_B

denote the respective sums to infinity. c. (iii) Determine the numerical difference

S_A-S_B

. State your result correct to two decimal places.