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**Ragnarok** This is from a discrete math textbook, but obviously calculus-based, so I'm asking it here.

Let $\displaystyle s_1,\ldots ,s_n$ be a sequence satisfying

(a) $\displaystyle s_1$ is a positive integer and $\displaystyle s_n$ is a negative integer.

(b) For all $\displaystyle i$, $\displaystyle 1\leq i<n$, $\displaystyle s_{i+1}=s_i+1$ or $\displaystyle s_{i+1}=s_i-1$.

Prove that there exists $\displaystyle i$, $\displaystyle 1<i<n$, such that $\displaystyle s_i=0$.

I thought about doing proof by contradiction, but I can't work anything out. I do not remember or never came across the regular calculus version of this theorem. Can anyone help?