Geometric Progression of Squares
Source:
February 1, 2009
geometric sequencegeometric series
Problem Statement
The limit of the sum of an infinite number of terms in a geometric progression is \frac {a}{1 \minus{} r} where denotes the first term and \minus{} 1 < r < 1 denotes the common ratio. The limit of the sum of their squares is:
(A)\ \frac {a^2}{(1 \minus{} r)^2} \qquad(B)\ \frac {a^2}{1 \plus{} r^2} \qquad(C)\ \frac {a^2}{1 \minus{} r^2} \qquad(D)\ \frac {4a^2}{1 \plus{} r^2} \qquad(E)\ \text{none of these}