- #1

vrbke1007kkr

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## Homework Statement

Let s

_{1}=1 and for n>=1 let s

_{n+1}=sqrt(s

_{n}+1)

Prove that the limit of this sequence is 1/2(1+Sqrt(5))

## Homework Equations

Show that there exist an N for every [tex]\epsilon[/tex]> 0, such that n>N implies

|S

_{n}-1/2(1+Sqrt(5))|< [tex]\epsilon[/tex]

## The Attempt at a Solution

I can prove that s is a increasing sequence bounded above thus s converges to a real number, but how to manipulate the terms inside the absolutely value takes a little more than conventional wisdom.

At first we realize that: s

_{n+1}

^{2}= s

_{n}+1, and since we are dealing with an increasing sequence, we can find a bound for s

_{n}, but can't see how that's useful

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