- #1

DKnight768

- 4

- 0

## Homework Statement

Use the ratio test to find if [tex]\sum\frac{1}{log(n)}[/tex] converges.

## Homework Equations

[tex]\sum\frac{1}{log(n)}[/tex]

## The Attempt at a Solution

Well, I tried [tex]\frac{a_{n+1}}{a_{n}}[/tex] and got [tex]\frac{log(n)}{log(n+1)}[/tex].

I can also try [tex]a_{n}=a_{n-1}[/tex] and then it's [tex]\frac{log(n-1)}{log(n)}[/tex], isn't it?

Maybe this is stupid, but can I remove the log() signs from the fraction? I can't, right?

I guess my problem is that I don't know how to compute the limit of [tex]\frac{log(n-1)}{log(n)}[/tex] as n becomes very large. log(n-1) is less than log(n), so maybe it's 0, and since the condition is that c is 0<c<1 it does not converge? I'm not confident at all in that answer. Please help

PS: I hope the latex symbols show up allright...