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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

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