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Putnam 2015 A4

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December 6, 2015
PutnamPutnam 2015

Problem Statement

For each real number x,x, let f(x)=∑n∈Sx12nf(x)=\sum_{n\in S_x}\frac1{2^n} where SxS_x is the set of positive integers nn for which ⌊nx⌋\lfloor nx\rfloor is even.
What is the largest real number LL such that f(x)≥Lf(x)\ge L for all x∈[0,1)x\in [0,1)?
(As usual, ⌊z⌋\lfloor z\rfloor denotes the greatest integer less than or equal to z.z.
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