What is the sum from x=0 to infinity of (x^x)/(x!) ?

The sum from x=0 to infinity of (x^x)/(x!) is diverges

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sum from x=0 to infinity of (x^x)/(x!)

x = 0 \sum \infty \frac{x ^{x}}{x !}

diverges

Solution steps

x = 0 \sum \infty \frac{x ^{x}}{x !}

Apply Series Ratio Test:

diverges

= diverges

n = 0 \sum \infty \frac{n}{n ^{2} + 3}

k = 1 \sum \infty \frac{4}{k ( k + 2 )}

n = 1 \sum \infty 7 (0.5)^{n - 1}

n = 2 \sum \infty \frac{4}{5 ^{n}}

n = 0 \sum \infty \frac{5}{1 + 9 n ^{2}}

What is the sum from x=0 to infinity of (x^x)/(x!) ?
The sum from x=0 to infinity of (x^x)/(x!) is diverges