What is the sum from n=5 to infinity of (ln(n))/n ?

The sum from n=5 to infinity of (ln(n))/n is diverges

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sum from n=5 to infinity of (ln(n))/n

n = 5 \sum \infty \frac{ln ( n )}{n}

diverges

Solution steps

n = 5 \sum \infty \frac{ln ( n )}{n}

Apply Series Integral Test:

diverges

= diverges

n = 1 \sum \infty 3^{- 3 n}

n = 3 \sum \infty 4 (\frac{1}{2})^{n + 2}

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

n = 1 \sum \infty 5 n^{2} e^{- n^{3}}

n = 1 \sum \infty n e^{- 4 n^{2}}

What is the sum from n=5 to infinity of (ln(n))/n ?
The sum from n=5 to infinity of (ln(n))/n is diverges