Hi,

I'm trying to prove the following limit

as x approaches infinity.

I'm getting stuck on the expansion of

I know that it's supposed to be

but I can't work out the series.

Can anyone help?

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- Mar 26th 2010, 09:19 AMthepopasmurfFinding limit of function using series expansion
Hi,

I'm trying to prove the following limit

as x approaches infinity.

I'm getting stuck on the expansion of

I know that it's supposed to be

but I can't work out the series.

Can anyone help? - Mar 26th 2010, 09:31 AMLaurent
- Mar 26th 2010, 10:01 AMthepopasmurf
Oh I see. Thanks. But why does it not work when I try to evaluate the expansion directly?

- Mar 26th 2010, 11:32 AMLaurent
You mean write the series expansion, for , where ? Then you have to justify that the last series converges to 0 when . There are ways to do that (this is an alternate series so we can get a uniform bound for the remainder of the series by Leibniz theorem), but it is not trivial, and first of all the asymptotic expansion is so much more appropriate (it is

*dedicated*to computation of limits).