Taylor series representation help

[monkeylord]

Homework Statement

Find the Taylor Series of x^(1/2) at a=1

Homework Equations

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

The Attempt at a Solution

i got the expansion and here's my attempt at the representation

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

 

[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 $x^{1/2}$?