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

Show that [itex] \sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}} [/itex]

converges and find the limit.

3. The attempt at a solution

I can write it also like this correct

[itex] 2^{\frac{1}{2}},2^{\frac{1}{2}}2^{\frac{1}{4}},2^{\frac{1}{2}}2^{\frac{1}{4}}2^{\frac{1}{8}} [/itex]

so each time i multiply it by the new number it is getting closer to 1.

Every new number on the end of the sequence is getting closer to 1 that I am multiplying it by. so this sequence is bounded and decreasing therefore it must have a limit.

Im not sure what it converges to. but when I know I need to show that it that the sequence

A-b<ε , where A is the sequence and b is the limit.

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# Homework Help: Convergence of a sequence.

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