sum of infinite series

iDoof

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Oct 17, 2005
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SUM of (3^n)/((5^n)*n!) from n=0 to infinity.

how do you find the sum this series converges to? i'm shaky with the whole thing to begin with, but i thought you just take the limit of the nth term, right? But how do I handle the factorial?


thanks so much guys
 
When you've got factorials, the Ratio Test is often useful. Have you tried that?

(The limit of the n-th term, being (3/5)<sup>n</sup>/n!, will clearly be zero, but this doesn't give you a limit of the sum of the terms; it only hints that such a sum might exist.)

Eliz.
 
Have you yet confirmed that the sum exists?

Eliz.
 
For all x, \(\displaystyle e^x = \sum\limits_{k = 0}^\infty {\frac{{x^k }}{{k!}}}\)

Does that look like your series? If x=3/5 what do you have?
 
ah! i get it now. i have to relate it to a taylor expansion that i know....


thanks so much for your replies everyone!!
 
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