1951 AHSME Problems/Problem 11
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Problem
The limit of the sum of an infinite number of terms in a geometric progression is where
denotes the first term and
denotes the common ratio. The limit of the sum of their squares is:
Solution
Let the original geometric series be . Therefore, their squares are
, which is a geometric sequence with first term
and common ratio
. Thus, the sum is
.
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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