(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\sum\limits_{i=0}^\infty \frac{i!}{5^i}[/tex]

2. Relevant equations

3. The attempt at a solution

(1) [tex]\sum\limits_{i=0}^\infty \frac{i!}{5^i}[/tex]

(2) [tex] = \lim_{i\rightarrow \infty}|{\frac{(i+1)!}{(5+1)^i} \cdot \frac{5^i}{i!}|[/tex]

(3) [tex] = \lim_{i\rightarrow \infty}{\frac{(i+1)!}{5i!}[/tex]

Could someone explain to me the jump from (2) to (3)? I can't make sense of it and my lecture notes don't mention anything in particular. Do the properties of factorials come into play here (I never learned factorials)?

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# Homework Help: Algebra behind the ratio test?

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