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Homework Statement
Given the sequence {a(n)}, which is refined recursively by
a(1)=1, a(n+1)=√(1+a(n))
Prove that the sequence converges and find it's limit.
Homework Equations
The Attempt at a Solution
I proved that it converges with two pretty easy induction cases.
I've also found what it converges to, the golden ratio w/ a calculator. How would I go about this not using a calculator? Usually one would just consider the infinite case but here I'm not sure how to do that.
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