## cherrilyn 5 years ago Determine convergence or divergence and explain which method you used for......

1. cherrilyn

$\sum_{n=2}^{\infty} 1/ n \ln n-n$

2. anonymous

the whole term in in denominator?

3. cherrilyn

no.. sorry I don't know how to make a division sign on here...... but its 1 over nln-n

4. anonymous

thats what i want to confirm

5. cherrilyn

yeah. 1 is in the numerator.

6. anonymous

have u read the integral test for convergence of the series?

7. cherrilyn

If $\int\limits_{1}^{\infty} f(x)dx$ converges then $\sum_{n=1}^{\infty} a _{n}$ converges

8. anonymous

right and function must be montonically decreasing

9. anonymous

$\int\limits_{2}^{\infty} (1/x)/(\ln x-1) dx$

10. cherrilyn

?

11. anonymous

solve the integral, the given series converges if the integral converges

12. anonymous

$\lim t \rightarrow \infty [\ln(lnx-1)] x varies from 2 \to t$