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I am solving a limit proof that has the following attached solution.

Question: Assume all s_{n}≠ 0. and that the limit L = lim abs(s_{n+1}/s_{n}) exists. Show that if L<1. the lim s_{n}=0

I Understand the solution except for one part which is also attached..

s_{n}= s_{N}*s_{N+1}/s_{N}*** s_{n}/s_{n-1}

Can someone please explain this portion of the problem? I don't understand how s_{N+2}cancels with s_{n-1}.. It definitely has something to do with n≥N but how they derived it I am not sure

Thanks

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# Limit Proof Confusion

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