Taylor Series

**cassie00** · April 27th 2008, 03:24 PM

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

**PaulRS** · April 27th 2008, 04:02 PM

Try proving the general case.

Given a real number $u$ and a natural number $n$ we define: $\binom{u}{n}=\frac{u\cdot{(u-1)\cdot{...\cdot{(u-n+1)}}}}{n!}$

The Binomial Theorem states that:

$(1+x)^u=\sum_{n=0}^{\infty}{\binom{u}{n}\cdot{x^n} }$

$|x|<1$

Note that if u is natural then the formula reduces to the famous: $(1+x)^u=\sum_{n=0}^{u}{\binom{u}{n}\cdot{x^n}}$

**TheEmptySet** · April 27th 2008, 04:05 PM

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

**cassie00** · April 27th 2008, 04:26 PM

Originally Posted by TheEmptySet

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

I'm sorry

. It won't happen again.

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