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[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