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Putnam 2002 A6

Source:

December 8, 2008
Putnamgeometryintegrationlogarithmsfunctioncollege contestsPutnam calculus

Problem Statement

Fix an integer b≥2 b \geq 2. Let f(1) \equal{} 1, f(2) \equal{} 2, and for each n≥3 n \geq 3, define f(n) \equal{} n f(d), where d d is the number of base-b b digits of n n. For which values of b b does \sum_{n\equal{}1}^\infty \frac{1}{f(n)} converge?
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