# SAT1000 - P876

Given that an infinite sequence $\{a_n\}$ consists of $k$ distinct values, $S_n=\displaystyle \sum_{i=1}^n a_i$.

If $\forall n \in \mathbb N^+$, $S_n \in \{2,3\}$, then find the maximum of $k$.

Have a look at my problem set: SAT 1000 problems

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