Question

determine if series is absolutely convergent.

sum from 1 to infinity (-6)^n/n!

Here's what I did so far

lim as n approaches infinity (-6)^(n+1)/ (n+1)! x n!/(-6)^n

I did some canceling and got

limit as n approaches infinity absolute value of -6n!/ (n+1)!

When i plug in n for infinity i got a indeterminate form. Answer suppose to be absolutely convergent. what did i do wrong. Help!

Answer 1

Cancel out the factorials: (n+1)!=(n+1)n!

Answer 2

where did you get the extra n?

Answer 3

The definition of the factorial is
n! = n * (n-1) * (n-2) ... 3*2*1
The product has to have exactly n factors.
This means that the factorial of n+1 has one more factor in it:
(n+1)! = (n+1) * n * (n-1) * (n-2) ... 3*2*1
Since the last n factors are what we call n!, we can write
(n+1)! = (n+1) * n!