What is the sum from n=1 to infinity of (31)/(n!) ?

The sum from n=1 to infinity of (31)/(n!) is converges

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sum from n=1 to infinity of (31)/(n!)

n = 1 \sum \infty \frac{31}{n !}

converges

Solution steps

n = 1 \sum \infty \frac{31}{n !}

Apply the constant multiplication rule:

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

= 31 \cdot n = 1 \sum \infty \frac{1}{n !}

Apply Series Ratio Test:

converges

= 31 converges

= converges

What is the sum from n=1 to infinity of (31)/(n!) ?
The sum from n=1 to infinity of (31)/(n!) is converges