Compute the Taylor series of (1-x)^(-1/2) by Taylor's formula.
I used Taylor's formula to get the first few terms but couldn't see a reasonable pattern to generalize...
Any help at all is appreciated
Try proving the general case.
Given a real number $\displaystyle u $ and a natural number $\displaystyle n$ we define: $\displaystyle \binom{u}{n}=\frac{u\cdot{(u-1)\cdot{...\cdot{(u-n+1)}}}}{n!}$
The Binomial Theorem states that:
$\displaystyle (1+x)^u=\sum_{n=0}^{\infty}{\binom{u}{n}\cdot{x^n} }$
$\displaystyle |x|<1$
Note that if u is natural then the formula reduces to the famous: $\displaystyle (1+x)^u=\sum_{n=0}^{u}{\binom{u}{n}\cdot{x^n}}$
http://www.mathhelpforum.com/math-he...or-series.html
Please don't double post
It just makes more work for everyone.
I gave you the formual for the nth derivative(The long way)
Try it and see what happens