Not sure what they want here, please help.

show funcion f(x) = n=0->infinity x^n / n!

show that f(x) = e^x

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- Feb 5th 2009, 11:30 AMrcmangoshow funcion is solution of differential function.
Not sure what they want here, please help.

show funcion f(x) = n=0->infinity x^n / n!

show that f(x) = e^x - Feb 5th 2009, 01:18 PMRincewind
Depends what you can use. If you can just use a Taylor series this is straightforward...

A Taylor's series is

$\displaystyle f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n.$

where $\displaystyle f^{(n)}(a)$ means the nth derivative of f(x) evaluated at x=a. So in your case

$\displaystyle f^{(n)}(x) = e^x$

and you substitute a=0 to get the result you need.

Note: A Taylor series with a=0 is also called a Maclaurin series.

Hope this helps.