- #1
RadiationX
- 256
- 0
I'm supposed to compare the series
[tex]\sum_{n=0}^{\infty}\frac{1}{n!}[/tex]
to some other series to see if the one above converges or diverges. I have no idea of what to compare it to.
I know by the ratio test that the above series converges, that is if I'm doing the ratio test correctly.
[tex]\lim_{n\rightarrow\infty}\frac{1}{(n+1)!}n!\\=\frac{1}{n(n+1)}(1*n)=\\\frac{1}{(n+1)}[/tex]
since this limit is zero which is less than one the series converges
[tex]\sum_{n=0}^{\infty}\frac{1}{n!}[/tex]
to some other series to see if the one above converges or diverges. I have no idea of what to compare it to.
I know by the ratio test that the above series converges, that is if I'm doing the ratio test correctly.
[tex]\lim_{n\rightarrow\infty}\frac{1}{(n+1)!}n!\\=\frac{1}{n(n+1)}(1*n)=\\\frac{1}{(n+1)}[/tex]
since this limit is zero which is less than one the series converges