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

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

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

n = 0 \sum \infty 5^{n} 4^{- n}

k = 1 \sum \infty 5^{- k}

n = 1 \sum \infty n (\frac{- 5}{9})^{n}

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