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

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

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

k = 1 \sum \infty \frac{k ^{k}}{k !}

diverges

Solution steps

k = 1 \sum \infty \frac{k ^{k}}{k !}

Apply Series Ratio Test:

diverges

= diverges

k = 5 \sum \infty \frac{1}{k ^{2} - 5 k + 6}

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

n = 0 \sum \infty 5 + (- 1)^{n}

n = 0 \sum \infty e^{n^{2}}

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

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