# Taylor's Theorem with Remainder

• May 2nd 2009, 02:33 PM
Truthbetold
Taylor's Theorem with Remainder
http://mathworld.wolfram.com/images/...dEquation1.gif

But, I'm not understanding the Lagrange Remainder.

http://mathworld.wolfram.com/images/...dEquation3.gif

for some http://mathworld.wolfram.com/images/...er/Inline3.gif

Here's a problem:
"Use the Lagrange form of the remainder to prove that the Maclaurin series converges to the generating function from the given function"

x* e^x

I got the Maclaurin series of that function.

$xe^x= x + x^2 + \frac{x^3}{2!}$

or
x^(n+1)/n! with the proper sum notation.

What I don't get is how to put this into the equation at the top. I might be able to correctly put a few things in the formula, such as the function, but I don't know how to solve or finish it.

Thanks!