## anonymous 5 years ago need to find if converges or diverges using ratio test: sum of all (ln(n))/(n) when n=1 to inf *not sure what cancels once RT is set up

1. anonymous

any idea?

2. anonymous

...why the ratio test? painful.

3. anonymous

The ratio I get using the ratio test is 1. It wouldn't be a conclusive test.

4. anonymous

If you want me to show you that, let me know.

5. anonymous

it's not that painful loki all you've got to do is put : an+1 / an , I find it rather simple lol ^_^

6. anonymous

Yeah, I know ;)

7. anonymous

:)

8. anonymous

$|\frac{\ln (n+1))}{n+1}/\frac{\ln(n)}{n}|=\frac{\ln(n+1)}{\ln(n)}\frac{n}{n+1}$This is an indeterminate form (infty/infty), so you can use L'Hopital's rule:$\lim_{n->\infty}\frac{\ln (n+1)}{\ln(n)}\frac{n}{n+1}=\lim_{n->\infty}\frac{\ln (n+1)}{\ln (n)}\lim_{n->\infty}\frac{n}{n+1}$$=\lim_{n->\infty}\frac{\frac{1}{n+1}}{\frac{1}{n}}\lim_{n->\infty}\frac{1}{1}=\lim_{n->\infty}\frac{n}{n+1}=\lim_{n->\infty}\frac{1}{1+\frac{1}{n}}=1$