Evaluation of a limit as n approaches infinity using L'Hopital's Rule

**PROBLEM:**

http://www.mymathforum.com/cgi-bin/mimetex.cgi?(x_{n})-series of numbers where:

x_0 = 1

and,

http://www.mymathforum.com/cgi-bin/m... sqrt(2+x_{n})

Find: http://www.mymathforum.com/cgi-bin/m...x_{n} - 2) = ?

**ATTEMPT:**

So far,

http://www.mymathforum.com/cgi-bin/m...,.\sqrt{3}}}}}

http://www.mymathforum.com/cgi-bin/m...^2\,=\,2\,+\,y

http://www.mymathforum.com/cgi-bin/m...arrow\,y\,=\,2

L'Hopital's rule:

http://www.mymathforum.com/cgi-bin/m...\frac{1}{4^n}}

http://www.mymathforum.com/cgi-bin/m...4^{2n}}}\,=\,0

http://www.mymathforum.com/cgi-bin/m...{n}\,-\,2) = 0

My application of L'Hopital's rule is incorrect. It's an indeterminate form, but not resolved in the way I indicated. Any ideas on how I could resolve the problem?

Re: Evaluation of a limit as n approaches infinity using L'Hopital's Rule

To use LaTeX on this forum, you need to put the code in tex tags, which look like [ tex ] [ / tex ] without the spaces.

Re: Evaluation of a limit as n approaches infinity using L'Hopital's Rule

I stripped out the mimetex stuff and was able to make the question readable:

In the last step you substituted 0 for . But it is not true that for all n, so you can't make that substitution.

I put the problem into Excel, and it looks like the limit should be about -1.097, but I can't see how to get to that result algebraically. Can someone else help?

- Hollywood

Re: Evaluation of a limit as n approaches infinity using L'Hopital's Rule

Sorry I tested on my maple the answer is :

Is there a way to show that this limit can be found mathematically?

How can one find limit of

using math(without the help of computer) where ?

Re: Evaluation of a limit as n approaches infinity using L'Hopital's Rule

Thank you all for trying to help.

And sorry for the trouble of reading this post; I just now started learning LaTeX.

Here's the solution:

Put to get and

Therefore,

Thus,

Hence,