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Viluxent Set 1 Paper 1 · Q12

Paper 1Sequences & seriesNumber & counting

For a positive integer nn, let d(n)d(n) denote the number of digits in the decimal representation of nn (so d(7)=1d(7)=1, d(58)=2d(58)=2, d(100)=3d(100)=3, and so on). For how many integers C>1C>1 does

∑n=1∞C−d(n)\sum_{n=1}^{\infty}C^{-d(n)}

evaluate to a positive integer?

A11
B22
C33
D44
E55
F99

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