- #1
tnutty
- 326
- 1
Homework Statement
Determine whether the series converges or diverges.
[tex]\sum\frac{37}{n!}[/tex]
I will just forget about the 37, and think of it as [tex]\sum\frac{1}{n!}[/tex]
I can try to decompose the n!
n! = n(n-1)!
n! = n ( n-1) (n-2)!
n! = n(n-1)(n-2)(n-3)...2*1
so [tex]\sum\frac{1}{n!}[/tex] = [tex]\sum\frac{1}{n(n-1)!}[/tex]
=
[tex]\frac{1}{n}[/tex] *[tex]\frac{1}{(n-1)!}[/tex]
since 1/n is a p-series and diverges so does the series.
Is this right ?