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HMMT — Sequence S_k=Σi·a_i with a_i=±1 Depending on S_{i-1}

2050SpecialistCombinatoricsAlgebraSequences & Series

13th Annual Harvard-MIT Mathematics Tournament

Let $S_{0}=0$ and let $S_{k}$ equal $a_{1}+2 a_{2}+\ldots+k a_{k}$ for $k \geq 1$. Define $a_{i}$ to be 1 if $S_{i-1}<i$ and -1 if $S_{i-1} \geq i$. What is the largest $k \leq 2010$ such that $S_{k}=0$ ?
0 students attempted0% solvedRating 2050

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