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## Homework Statement

[tex]

\sum_{n = 2}^{\infty} \frac{1}{n*ln(n)}

[/tex]

I have to find whether the series absolute converge, conditionally converge or diverge?

**2. The attempt at a solution**

I used the ratio test.

so, lim(n to infinity) [n*ln(n)]/[(n+1)*ln(n+1)]

since ln (n+1) will be greater than ln (n) and n+1 will be greater than n, the whole denominator will be greater than the numerator so when i take the limit, the value must be less than 1.

but i think i have cancel n or ln(n) to show that the whole limit is really less than 1 to converge.

help!!!!

i m sorry . i dun know how to use the latex code..