- #1
wil3
- 179
- 1
Hello. For a physics course, I need to often make use of the binomial series and it's corollary, the expansion of:
[tex] \sqrt{1-x^2} [/tex]
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:
[tex] 1-\frac{x^2}{2}-\frac{x^4}{8}-\frac{x^6}{16}-...- \frac{x^{2n}}{2^n}[/tex]
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.
[tex] \sqrt{1-x^2} [/tex]
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:
[tex] 1-\frac{x^2}{2}-\frac{x^4}{8}-\frac{x^6}{16}-...- \frac{x^{2n}}{2^n}[/tex]
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.
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