What is the sum from n=0 to infinity of 3/(n!) ?

The sum from n=0 to infinity of 3/(n!) is converges

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sum from n=0 to infinity of 3/(n!)

n = 0 \sum \infty \frac{3}{n !}

converges

Solution steps

n = 0 \sum \infty \frac{3}{n !}

Apply the constant multiplication rule:

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

= 3 \cdot n = 0 \sum \infty \frac{1}{n !}

Apply Series Ratio Test:

converges

= 3 converges

= converges

n = 0 \sum \infty 2^{n + 1}

n = 0 \sum \infty 4 (\frac{1}{3})^{n}

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

n = 2 \sum \infty \frac{7}{n ( n + 2 )}

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

What is the sum from n=0 to infinity of 3/(n!) ?
The sum from n=0 to infinity of 3/(n!) is converges