How can we prove $e^{x+y}=e^{x}e^{y}$ by the power series $$e^{x}=\sum_{k=0}^{\infty}\dfrac{x^{k}}{k!}\,\,\,?$$
Is there any simple method?
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This may helps you. – Bumblebee Jul 23 '15 at 05:31
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its easier to use $e^x=\lim_\limits{n\to\infty} (1+\dfrac{x}{n})^\frac{1}{n}$ – JMP Jul 23 '15 at 05:37
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Thanks for the comments from apnorton, get it. – X Leo Jul 23 '15 at 05:39