What is the sum from n=1 to infinity of 1/(n*ln(n)) ?

The sum from n=1 to infinity of 1/(n*ln(n)) is diverges

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sum from n=1 to infinity of 1/(n*ln(n))

n = 1 \sum \infty \frac{1}{n \cdot ln ( n )}

diverges

Solution steps

n = 2 \sum \infty \frac{1}{n ln ( n )}

Apply Series Integral Test:

diverges

= diverges

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What is the sum from n=1 to infinity of 1/(n*ln(n)) ?
The sum from n=1 to infinity of 1/(n*ln(n)) is diverges