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

Find a sequence whose limit is [tex]\sqrt{2}[/tex].

2. Relevant equations

The work preceeding this was about using recurrence relations to find sequences with desired limits, so that's the method they want me to use.

3. The attempt at a solution

We can find the limit of the sequence given by

[tex]a_{n+1} = \frac{1}{2+a_{n}}[/tex] by noting that [tex]a_{n+1}[/tex] and [tex]a_{n}[/tex] both have the same limit. So we can write

[tex] l = \frac{1}{2+l} [/tex] and find the positive root of that: [tex]l = -1 + \sqrt{2}[/tex]. This is the limit of the sequence.

I can then just add on one to each term to give a sequence with limit [tex]\sqrt{2}[/tex]. Is this all they want me to do you think? Or is there a way to get write another sequence involving [tex]a_{n+1}[/tex] and [tex]a_{n}[/tex] which gives the desired answer?

Thanks.

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# Homework Help: Find a sequence convering to sqrt(2)

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