What is the sum from n=1 to infinity of (8n)/(n!) ?

The sum from n=1 to infinity of (8n)/(n!) is converges

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sum from n=1 to infinity of (8n)/(n!)

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Series Ratio Test:

converges

= 8 converges

= converges

\int_{0}^{l n (2)} x e^{- x} d x

x \to \infty lim (4 x^{2})

6 sin (- x)

n = 1 \sum \infty 4 (0.6)^{n - 1}

e^{x} - x^{4}

What is the sum from n=1 to infinity of (8n)/(n!) ?
The sum from n=1 to infinity of (8n)/(n!) is converges