Question

Determine convergence or divergence and explain which method you used for......

Answer 1

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

Answer 2

the whole term in in denominator?

Answer 3

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

Answer 4

thats what i want to confirm

Answer 5

yeah. 1 is in the numerator.

Answer 6

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

Answer 7

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

Answer 8

right and function must be montonically decreasing

Answer 9

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

Answer 10

?

Answer 11

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

Answer 12

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