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Determine whether the series is convergent or divergent.

$ \displaystyle \sum_{n = 2}^{\infty} \frac {1}{n \ln n} $

Divergent

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to do this problem. We're going to use the integral test because we have a continuous positive, decreasing function on this interval. So you want to evaluate integral from two to infinity of one over X Alan X check and I'm going to use the U substitution u equals Ellen acts. It gives me to you one over x dx so conveniently we have these all in are integral. So this becomes integral from some new end points of one over you to you, which will become Helen of you from the whatever those endpoints ended up being. And when we replace our use with exes, we will get the natural log of the natural law Vex evaluated from two to twenty. So we need to take a limit to deal with that infinity easily enough. And when we write this difference, we'LL see well that convergence or diversions looks like now Ellen of that should be non ex Buddy two now Alan of Ellen of twos. Just some number. But Ellen of Ellen of tea Asti goes to infinity also goes to infinity. So we know that our Siri's is diversion because the girl is diversion