What is the sum from k=1 to infinity of (1+2/k)^k ?

The sum from k=1 to infinity of (1+2/k)^k is diverges

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sum from k=1 to infinity of (1+2/k)^k

k = 1 \sum \infty (1 + \frac{2}{k})^{k}

diverges

Solution steps

k = 1 \sum \infty (1 + \frac{2}{k})^{k}

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty \frac{1}{n ^{0.8}}

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

n = 1 \sum \infty (\frac{6 π}{7})^{n}

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

n = 0 \sum \infty (- 9)^{n}

What is the sum from k=1 to infinity of (1+2/k)^k ?
The sum from k=1 to infinity of (1+2/k)^k is diverges