I just want to quickly check....

I used the integral test to check if $\displaystyle \sum_{n=2}^{\infty}\frac{1}{nln(n)} $converges.... and i found that it does. Can someone verify this? Thanks :)

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- Jan 10th 2009, 04:45 AMtsal15integral test
I just want to quickly check....

I used the integral test to check if $\displaystyle \sum_{n=2}^{\infty}\frac{1}{nln(n)} $converges.... and i found that it does. Can someone verify this? Thanks :) - Jan 10th 2009, 04:56 AMflyingsquirrel
- Jan 10th 2009, 04:59 AMmr fantastic
- Jan 10th 2009, 05:01 AMProve It
- Jan 10th 2009, 05:08 AMmr fantastic
- Jan 10th 2009, 05:13 AMProve It
- Jan 10th 2009, 04:53 PMKrizalid
Always verify that $\displaystyle f$ must be positive, continuous and decreasing on $\displaystyle [1,\infty[.$ :)

- Jan 10th 2009, 05:10 PMtsal15
- Jan 13th 2009, 05:54 AMtsal15
Ok now, I've got a problem...

the integral equals => $\displaystyle ln(ln(x)$ with infinity and 2 being the bounds

therefore, $\displaystyle ln(ln(\infty)) - ln(ln(2))$

ln(ln(2)) is a value. Thus even if $\displaystyle ln(ln(\infty))$ does diverge, ln(ln(2)) will converge..... so does this change things? - Jan 13th 2009, 06:34 AMChop Suey
- Jan 13th 2009, 11:12 AMmr fantastic
- Jan 13th 2009, 02:56 PMProve It