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## Homework Statement

Let [tex]s_{1} = 1[/tex] and [tex]s_{n+1} = \sqrt{s_{n} + 1}[/tex] Assume this converges to [tex]\frac{1}{2}(1+\sqrt{5})[/tex] and prove it.

## Homework Equations

## The Attempt at a Solution

I'm not really sure where to begin. I tried to set it up with [tex]|s_{n} - s| < \epsilon[/tex] but I'm not sure how to handle the recursiveness of the sequence.

Any tips would be appreciated.