What is the sum from n=2 to infinity of 1/(nln(n^3)) ?

The sum from n=2 to infinity of 1/(nln(n^3)) is diverges

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sum from n=2 to infinity of 1/(nln(n^3))

n = 2 \sum \infty \frac{1}{n ln ( n ^{3} )}

diverges

Solution steps

n = 2 \sum \infty \frac{1}{n ln ( n ^{3} )}

Apply Series Integral Test:

diverges

= diverges

n = 0 \sum \infty \frac{i}{n !}

n = 1 \sum \infty 5^{n} i

n = 1 \sum \infty 5 (- \frac{1}{8})^{5 n}

n = 1 \sum \infty \frac{1}{n ^{2} + 25}

n = 4 \sum \infty (- 0.61)^{n}

What is the sum from n=2 to infinity of 1/(nln(n^3)) ?
The sum from n=2 to infinity of 1/(nln(n^3)) is diverges