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## Homework Statement

If {S_n} is a sequence whose values lie inside an interval [a,b], prove {S_n/n} is convergent.

We don't know Cauchy sequence yet. All we know is the definition of a bounded sequence, and convergence and divergence of sequences. Along with comparison tests and Squeeze theorem.

## Homework Equations

Limit of a sequence: abs(S_n - L) < Epsilon whenever n>=N, provided for Epsilon>0.

## The Attempt at a Solution

I see that every convergent sequence is bounded, but the opposite isn't always true, so how do I show that the smaller sequence is convergent given that {S_n} is bounded?