Taylor series for cartesian circle equation

[wil3]

Hello. For a physics course, I need to often make use of the binomial series and it's corollary, the expansion of:

$$\sqrt{1-x^2}$$

This probably sounds rather stupid, but for some reason, when I do a MacClaurin expansion of this series, I cannot seem to generate the correct series, which I know from texts to be:

$$1-\frac{x^2}{2}-\frac{x^4}{8}-\frac{x^6}{16}-...- \frac{x^{2n}}{2^n}$$

I keep on getting that the derivative evaluated at zero are zero, which, to me, suggests that there is some sort of trick to this series derivation that I am missing. Any advice?

Thank you very much.

 

[tiny-tim]

hello wil3!

(have a square-root: √ and try using the X² tag just above the Reply box )

… I keep on getting that the derivative evaluated at zero are zero, which, to me, suggests that there is some sort of trick to this series derivation that I am missing.

(this is √(1 - x²))

the odd derviatives should be zero, but not the even ones …

show us how you got the second derivative

 

[wil3]

...oh my, well that's embarrassing. I got it now. Thanks for pointing that out.

I also fixed the LaTex- still getting used to the syntax.

Thank you very much