What is the sum from n=1 to infinity of (n5^n)/(n!) ?

The sum from n=1 to infinity of (n5^n)/(n!) is converges

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sum from n=1 to infinity of (n5^n)/(n!)

n = 1 \sum \infty \frac{n 5 ^{n}}{n !}

converges

Solution steps

n = 1 \sum \infty \frac{n \cdot 5 ^{n}}{n !}

Apply Series Ratio Test:

converges

= converges

5 tan (x)

x (x - 14)

x \to 0 lim (e^{- x})

\frac{s - 1}{s ( s - 1 ) + 2}

\int e^{- (\frac{x}{2})^{2}} d x

What is the sum from n=1 to infinity of (n5^n)/(n!) ?
The sum from n=1 to infinity of (n5^n)/(n!) is converges