Mathematics

Problem

Consider a geometric progression whose first term is

12

and whose common ratio is

r=\dfrac{3m-2}{m+4}

, where

m

is a real parameter. a. (i) Determine all real values of

m

for which the corresponding infinite series converges. b. (ii) For the values of

m

found in part (i), obtain an expression for the sum to infinity in terms of

m

. c. (iii) Hence find the exact sum when

m=2