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

Test for convergence and divergence.

2. Relevant equations

[itex]\sum_{i=1}^{n} \frac{n!}{3^n}[/itex]

[itex]\sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}}[/itex]

3. The attempt at a solution

For the first one I get [itex]\frac{(n+1)}{3}[/itex] After applying the ratios. Taking the limit as n approaches infinity, it is greater than 1, so it should diverge. But the book says it converges.

For the second one, I think we have to take the (1/n)th root, which converts it to [itex]\sum_{i=1}^{n} \frac{1}{(log (n))}[/itex]. Is this correct resoning?

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# Homework Help: Ratio and root tests

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