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- #1

#### skatenerd

##### Active member

- Oct 3, 2012

- 114

_{n}defined recursively by:

a

_{1}=1

and

a

_{n+1}= \(\frac{a_n}{2}\) + \(\frac{1}{a_n}\)

First part was the only part i know how to do. it was to find a

_{n}for n=1 through 5.

However this next part has me stumped. Assume that:

The limit as n approaches infinity = alpha > 0

Obtain the value alpha by taking the limit of both sides of (1) [(1) is the info given in the beginning].

Now I can already tell this limit is going to \(\sqrt{2}\) because it is kind of hinted to in the later parts of this problem. However I am kind of confused as to how to approach doing this limit of both sides of a

_{n+1}= \(\frac{a_n}{2}\) + \(\frac{1}{a_n}\) . How would I evaluate this limit when the right side of the equation is in terms of a

_{n}?