# Power Series w/ factorial

• April 8th 2009, 08:12 PM
mollymcf2009
Power Series w/ factorial
Can someone check to see if I evaluated this correctly?

$\sum^{\infty}_{n+1} \frac{n!x^n}{8\cdot 17\cdot 26\cdot ...(9n-1)}$

$= \sum^{\infty}_{n+1} \frac{n!x^n}{(9n-1)!}$

Is that right?
• April 8th 2009, 08:18 PM
Jhevon
Quote:

Originally Posted by mollymcf2009
Can someone check to see if I evaluated this correctly?

$\sum^{\infty}_{n+1} \frac{n!x^n}{8\cdot 17\cdot 26\cdot ...(9n-1)}$

$= \sum^{\infty}_{n+1} \frac{n!x^n}{(9n-1)!}$

Is that right?

no

(9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)
• April 8th 2009, 08:36 PM
mollymcf2009
Quote:

Originally Posted by Jhevon
no

(9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)

• April 8th 2009, 08:38 PM
mollymcf2009
Quote:

Originally Posted by Jhevon
no

(9n - 1)! = (9n - 1)(9n - 2)(9n - 3)....(3)(2)(1)

• April 8th 2009, 08:54 PM
Chris L T521
Quote:

Originally Posted by mollymcf2009

It doesn't work for values of $n\geqslant3$!! XD

What in particular are you asked to do with this series? Show that it converges??
• April 8th 2009, 09:01 PM
mollymcf2009
Quote:

Originally Posted by Chris L T521
It doesn't work for values of $n\geqslant3$!! XD

What in particular are you asked to do with this series? Show that it converges??

Find the radius of convergence and the interval of convergence.

I don't know a good way to rewrite factorials. Do I need to do that before I try to evaluate this? Thanks Chris!
• April 8th 2009, 09:08 PM
Jhevon
Quote:

Originally Posted by mollymcf2009
Find the radius of convergence and the interval of convergence.

I don't know a good way to rewrite factorials. Do I need to do that before I try to evaluate this? Thanks Chris!

if that's the case, why not use the ratio or root test? you don't need to rewrite anything. probably the ratio test will be easier here

however, in general, you can use Stirling's approximation.
• April 8th 2009, 09:45 PM
matheagle
Do you mean n=1 instead of n+1?