1. ## Maclaurin Series Problem

Hi,

I'm having trouble finding the Maclaurin series using a known series. I can find the series using the Maclaurin formula but I can't do it using a known series. Does anyone have any idea on which series to use and how I can use it. The series the I have considered was the Binomail series but I cant seem to get it to work for this problem.

Thanks, DLL.

2. Yep. Write: $f(x) = \frac{1}{\sqrt{4-x}} = \left(4-x\right)^{-\frac{1}{2}} = \left[4\left(1 - \tfrac{x}{4}\right)\right]^{-\frac{1}{2}}$ ${\color{white}.} \ \Rightarrow \ f(x) = \tfrac{1}{2} \left(1 - \tfrac{x}{4}\right)^{-\frac{1}{2}}$

From an old post:

Recall that binomial series are given by: $(1+y)^k = 1 + ky + \frac{k(k-1)}{2!}y^2$ ${\color{white}.} \ + \ \frac{k(k-1)(k-2)}{3!}y^3 + \cdots + \frac{k(k-1)(k-2)\cdots(k - n+1)}{n!}y^n + \cdots$

for any $k \in \mathbb{R}$ and if $|y| < 1$. Here, $y = (-1)\tfrac{x}{4}$ and $k = -\tfrac{1}{2}$ .