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Determine or find out if the following series is convergent or divergent.
Solution
In this example the function we'll use is,
f (x) = 1 / (x ln x)
This function is visibly positive and if we make x larger the denominator will obtain larger and thus the function is also decreasing. Hence, all we need to do is find out the convergence of the following integral.
The integral is divergent and thus the series is as well divergent by the Integral Test.
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