I have the converging series:

$$ 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!}+... $$

and I'm trying to find its sum when x = .9. I know this is the Taylor series for some function$f(x)$, and that I can use $f(x)$ to find the sum, but I'm not sure which function to use. It looks very much like the taylor series for $e^x$, but it's alternating. Is there some sort of composition of functions I should use? Can someone point me in the right direction?

  • $\begingroup$ Try thinking of this as a function of $-x$ instead... $\endgroup$ – Semiclassical Sep 5 '14 at 18:49
  • 2
    $\begingroup$ What is $$e^{-x}?$$ $\endgroup$ – lab bhattacharjee Sep 5 '14 at 18:49

$$ e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+....\\turn\\x\\to \\-x\\so\\e^{-x}=1-x+\frac{(-x)^2}{2!}+\frac{(-x)^3}{3!}+\frac{(-x)^4}{4!}+....\\so\\e^{-0.9}$$


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