Originally Posted by

**Harry1W** I'm looking to find an expression for the $\displaystyle n^{th}$ term of the Taylor Series for $\displaystyle (1+x)^{\frac{1}{2}} $.

I have found that:

$\displaystyle (1+x)^{\frac{1}{2}} = 1 + \frac{1}{1!} \left( \frac{1}{2} \right) x +\frac{1}{2!} \left( \frac{1}{2} \right) \left( \frac{-1}{2} \right) x^2 + \frac{1}{3!} \left( \frac{1}{2} \right) \left(\frac{-1}{2} \right) \left( \frac{-3}{2} \right) x^3 + \ldots $

The first term (1) is the only term that I can't get to fit the suggested general term:

$\displaystyle \frac{1}{(n - 1)!} \displaystyle\prod_{i = 1}^n \left( \frac{5 - 2i}{2} \right) $

Any suggestions much appreciated, as this is really bugging me!