I am trying to solve the problem and but i am stuck.. Can someone please have look and help out...

Problem

if and where |a| <1 and |b| < 1. Prove that

Solution

GP Series

Similarly

taking LHS of the equation

using GP

RHS of the equation

If I substitute 1 and 2 in 4,i get

this is no where near to equ 4. My approach might be wrong. please suggest if possible...