So i have a function:
$$f:(-1,1) \rightarrow \mathbb{R} , f(x)= \frac{1}{\sqrt{(1-x)^3}}$$

I need to calculate it's taylor series(Maclaurin to be exact, because it's to be centered around x=0). And use that to either prove either disprove the following inequality(i presume it will be of help, i could be wrong though):
$$\sqrt{1-x} \sum\_{n=0}^{\infty} \frac{x^n}{(2n)!!} \leq \frac{1}{1-x} $$

[double factorial meaning, so there is no confusion](https://en.wikipedia.org/wiki/Double_factorial)

Any help would be appreciated, thank you in advance.