1965 AHSME Problems/Problem 24
Problem
Given the sequence , the smallest value of n such that the product of the first members of this sequence exceeds is:
Solution
Note that the given sequence is a geometric sequence with a common ratio . Let the product of the first terms of the sequence be denoted . It is a consequence of the laws of exponents that , , and, in general, , where denotes the th triangular number. Setting equal to , we see that:
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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