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Question

The limit of the sum of an infinite number of terms in a geometric progression is a1 - r where a denotes the first term and - 1 < r < 1 denotes the common ratio. The limit of the sum of their squares is:

Accepted Answer

Let the original geometric series be a,ar,ar^2,ar^3,ar^4. Therefore, their squares are a^2,a^2r^2,a^2r^4,a^2r^6,, which is a geometric sequence with first term a^2 and common ratio r^2. Thus, the sum is a^21 - r^2.