What is the sum from n=1 to infinity of (18^n)/(n!) ?

The sum from n=1 to infinity of (18^n)/(n!) is converges

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sum from n=1 to infinity of (18^n)/(n!)

n = 1 \sum \infty \frac{1 8 ^{n}}{n !}

converges

Solution steps

n = 1 \sum \infty \frac{1 8 ^{n}}{n !}

Apply Series Ratio Test:

converges

= converges

k = 0 \sum \infty (\frac{k}{k + 15})^{k}

k = 1 \sum \infty \frac{1}{k ^{6}}

k = 0 \sum \infty (0.8)^{k}

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

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

What is the sum from n=1 to infinity of (18^n)/(n!) ?
The sum from n=1 to infinity of (18^n)/(n!) is converges