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1951 AMC 12 Question 11

AMC12 · 1951 AMC 12

Question 11

The limit of the sum of an infinite number of terms in a geometric progression is $\dfrac{a}{1-r},$ where $a$ denotes the first term and $-1\lt r\lt1$ denotes the common ratio. The limit of the sum of their squares is:
  1. $\dfrac{a^2}{(1-r)^2}$
  2. $\dfrac{a^2}{1+r^2}$
  3. $\dfrac{a^2}{1-r^2}$
  4. $\dfrac{4a^2}{1+r^2}$
  5. None of these