1953 AHSME Problems/Problem 27
Problem
The radius of the first circle is inch, that of the second inch, that of the third inch and so on indefinitely. The sum of the areas of the circles is:
Solution
Note the areas of these circles is , , . The sum of these areas will thus be . We use the formula for an infinite geometric series to get the sum of the areas will be , or .
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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