Problem: The limit of the sum of an infinite number of terms in a geometric progression is 1−ra where a denotes the first term and −1<r<1 denotes the common ratio. The limit of the sum of their squares is:
Answer Choices:
A. (1−r)2a2
B. 1+r2a2
C. 1−r2a2
D. 1+r24a2
E. none of these
Solution:
The new series is a2+a2r2+a2r4+⋯;∴S=a2/(1−r2).