- #1
zonk
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Homework Statement
Test for convergence and divergence.
Homework Equations
[itex]\sum_{i=1}^{n} \frac{n!}{3^n}[/itex]
[itex]\sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}}[/itex]
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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