The task is to show why e^2x = (1+2x/n)^n for very large n. I'm not sure how to tackle this problem. I thought about creating the generating functions and doing some algebraic manipulation but couldn't finish it.
The task is to show why e^2x = (1+2x/n)^n for very large n. I'm not sure how to tackle this problem. I thought about creating the generating functions and doing some algebraic manipulation but couldn't finish it.
Suppose , then expand the RHS using the binomial
expansion and compare with the power series expansion of the LHS.
The task is to show why e^2x = (1+2x/n)^n for very large n. I'm not sure how to tackle this problem. I thought about creating the generating functions and doing some algebraic manipulation but couldn't finish it.
Another method is to define:
then
which is of seperable type so:
or:
and as (though a bit of care may be needed to show this)
Hence for fixed we have:
RonL
Last edited by CaptainBlack; Jul 17th 2007 at 01:15 PM.