Taylor series representation help

1. May 21, 2014

monkeylord

1. The problem statement, all variables and given/known data
Find the Taylor Series of x^(1/2) at a=1

2. Relevant equations
i have no idea how to do the representation, i believe our professor does not want us to use any binomial coefficients

3. The attempt at a solution
i got the expansion and heres my attempt at the representation

1+∑(1 to ∞) [(-1)(-3)...(-(2n+1))/2^n](x-1)^n/(n!)

2. May 21, 2014

HallsofIvy

There are many different ways to "represent" a function as a series but the definition of the "Taylor series" representation of f(x) is
$$\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x- a)^n$$
where "$f^{(n)}(a)$" is the nth derivative of f at x= a. Have you found the nth derivative of $x^{1/2}$?

Last edited by a moderator: May 21, 2014