What is the sum from n=1 to infinity of (32)/(n!) ?

The sum from n=1 to infinity of (32)/(n!) is converges

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sum from n=1 to infinity of (32)/(n!)

n = 1 \sum \infty \frac{32}{n !}

converges

Solution steps

n = 1 \sum \infty \frac{32}{n !}

Apply the constant multiplication rule:

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

= 32 \cdot n = 1 \sum \infty \frac{1}{n !}

Apply Series Ratio Test:

converges

= 32 converges

= converges

n = 0 \sum \infty \frac{n}{n ^{2} + 7}

n = 1 \sum \infty 3^{- (n - 1)}

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

n = 1 \sum \infty \frac{10}{2 ^{n}}

n = 0 \sum \infty \frac{7}{4 - n ^{2}}

What is the sum from n=1 to infinity of (32)/(n!) ?
The sum from n=1 to infinity of (32)/(n!) is converges