sum of infinite series

[iDoof]

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

 

[stapel]

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)ⁿ/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.

 

[iDoof]

ah, but how do you find what that sum is?

 

[stapel]

Have you yet confirmed that the sum exists?

Eliz.

 

[pka]

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?

 

[iDoof]

ah! i get it now. i have to relate it to a taylor expansion that i know....


thanks so much for your replies everyone!!