Calculate MacLaurin Series for Finding the Sum of a Series | Homework Help

[dwdoyle8854]

Homework Statement

"Find the sum of the seires:

3 + (9/2!) + 27/3! +81/4!+ ... "

Homework Equations

e^x = Ʃ n=0 to inf (x^n)/n!

The Attempt at a Solution

=3(1 +3/2! + 9/3! + 27/4! + ...
=3*Ʃ n=0 to inf( (3^n)/(n+1)!)
=Ʃ n=0 to inf( (3^(n+1))/(n+1)!)

. unsure what to do from here, maybe break apart the sigma by re-indexing? I am not sure how to do this. Any help would be greatly appreciated.

 

[mfb]

Why did you pull out the 3? If you are missing the first term, I would add it manually in the sum (and subtract it outside). This is easier than an index shift.