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?
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).