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Homework Statement
Let s1=1 and for n>=1 let sn+1=sqrt(sn+1)
Prove that the limit of this sequence is 1/2(1+Sqrt(5))
Homework Equations
Show that there exist an N for every \epsilon> 0, such that n>N implies
|Sn-1/2(1+Sqrt(5))|< \epsilon
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: sn+12 = sn+1, and since we are dealing with an increasing sequence, we can find a bound for sn, but can't see how that's useful
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