What is the sum from k=0 to infinity of 2/(k!) ?

The sum from k=0 to infinity of 2/(k!) is converges

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sum from k=0 to infinity of 2/(k!)

k = 0 \sum \infty \frac{2}{k !}

converges

Solution steps

k = 0 \sum \infty \frac{2}{k !}

Apply the constant multiplication rule:

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

= 2 \cdot k = 0 \sum \infty \frac{1}{k !}

Apply Series Ratio Test:

converges

= 2 converges

= converges

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What is the sum from k=0 to infinity of 2/(k!) ?
The sum from k=0 to infinity of 2/(k!) is converges