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| + | We will start this from the beginning with the series: | ||
| + | <math>1+r+r^2+r^3+...+r^N=\frac{1}{1-r}-\frac{r^{N+1}}{1-r}</math> | ||
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| + | From here we substitute <math>r=-x^2</math> to get | ||
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| + | <math>1-x^2+x^4-x^6+...+(-1)^Nx^{2N}=\frac{1}{1+x^2}-\frac{(-1)^{N+1}x^{2(N+1)}}{1+x^2}</math> | ||
Revision as of 15:55, 26 October 2008
We will start this from the beginning with the series:
$ 1+r+r^2+r^3+...+r^N=\frac{1}{1-r}-\frac{r^{N+1}}{1-r} $
From here we substitute $ r=-x^2 $ to get
$ 1-x^2+x^4-x^6+...+(-1)^Nx^{2N}=\frac{1}{1+x^2}-\frac{(-1)^{N+1}x^{2(N+1)}}{1+x^2} $
