I have a recursive sequence given by xn=√1+xn−12, x1=0
I can easily show that it is increasing, bounded and thus converges with its limit being 1. But what if I wanted to upper bound xn0 for some fixed n0? This bound should be dependent on n. How should I proceed?
Answer
x0=cosπ2x1=cosπ4⋮xn=cos2−n−1π
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