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

The sum from n=1 to infinity of nln(1+1/n) is diverges

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sum from n=1 to infinity of nln(1+1/n)

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty 4^{3 - 3 n}

k = 1 \sum \infty \frac{k}{2 ^{k - 1}}

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

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

n = 0 \sum \infty 1 - \frac{1}{n}

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