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I have a sequence, [tex]\sqrt{2}[/tex], [tex]\sqrt{2 \sqrt{2}}[/tex], [tex]\sqrt{2 \sqrt{2 \sqrt{2}}}[/tex], ...

Basically, the sequence is defined as x1 = root 2

x(n+1) = root (2 * xn).

I need to show that this sequence converges and find the limit.

I proved by induction that this sequence increases. Since it increases, its bounded below by root 2. I need to show that it is bounded above by 2. Then I can use the Monotone Convergence Theorem to show that this sequence converges.

Any ideas?

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# Homework Help: Prove the upper bound

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