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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

"The Logarithmic p-series is defined by (sigma summation n=2 to infinity) of 1/(n(ln(n)))

^{p}) for p>0. Determine for which values of p it is convergent or divergent."

So off the bat I kind of assumed that to do this with a constant p, and seeing the series is decreasing and positive, I should use the integral test. Set up the integral of this series, and I made a substitution u for ln(n). this ended up with (u

^{-p+1})/(p+1) and I plugged the ln(n) back in and this is where I got kind of lost. Plugging in the limits of integration seemed to be a little messy, and I didn't really know where to go from there. If someone wants to give me a hint or a little guidance that would be nice. Thanks.