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could someone help me to find the sum of the series from zero to infinity (3^n/(5^n)n!)

MIT 18.02 Multivariable Calculus, Fall 2007
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If I understand your question correctly, you would like to know what is:\[\sum_{n=0}^{\infty} \frac{ 3^n }{ 5^n \times n! }\] If this is the case, then, the equation can be written as: \[\sum_{n=0}^{\infty} \frac{ (\frac{3}{5})^n }{n! }\] The Taylor series of e^x is: \[e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}\] Comparing the two equations, the answer would be e^(3/5) = 1.8221. Hope it helps!

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