Determine that the following series is convergent or diverge, Mathematics

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Determine or find out if the following series is convergent or divergent.

1226_Determine that the following series is convergent or diverge 2.png

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.

544_Determine that the following series is convergent or diverge 1.png

The integral is divergent and thus the series is as well divergent by the Integral Test.

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