(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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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# Homework Help: How would I find what a recursive sequence converges to a certain point?

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