I want to show that [itex] e^x e^x = e^{2x} [/itex] using a power series expansion. So I start with(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum_{n=0}^\infty \frac{x^n}{n!} \sum_{m=0}^\infty \frac{x^m}{m!} [/tex]

[tex] \sum_{n=0}^\infty \sum_{m=0}^\infty \frac{x^n}{n!} \frac{x^m}{m!} [/tex]

[tex] \sum_{n=0}^\infty \sum_{m=0}^\infty \frac{x^{m+n}}{m!n!} [/tex]

I am at a loss of where to go from here. I want to reduce the last expression down to [itex] \sum_{n=0}^\infty \frac{(2x)^n}{n!} [/itex] but I am not sure of how to get rid of one of the summations.

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# Exponential Power Series Expansion

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