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

Find the limit of the sequence

{ sqrt(2), sqrt(2sqrt(2)), sqrt(2sqrt(2sqrt(2))) ... }

2. Relevant equations

Limit Laws?

3. The attempt at a solution

I wrote out the first five values in the sequence and came to the conclusion that this sequence could be written out as

[tex]A_{n} = 2^\frac{2^{n}-1}{2^{n}}[/tex]

I then took [tex]\frac{2^{n}-1}{2^{n}}[/tex], broke it down to [tex]1 - \frac{1}{2^{n}}[/tex] which allowed me to rewrite the equation to [tex]2\times2^\frac{-1}{2^{n}}[/tex]. Ignoring the 2 for now, I re-worked the fraction exponent and resulted with [tex]-(\frac{1}{2})^{n}[/tex] and made the value into a fraction [tex]\frac{1}{2^(\frac{1}{2})^{n}}[/tex].

Using the sheer power of what is known as the graphing calculator, I was able to determine that the limit of that equation is 1, and then multiplying 2 to it gave 2. Without a calculator, how can I lay out the steps?

Note to self: BUY A TABLET!!

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# Homework Help: Limit of a sequence

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