What is the sum from k=1 to infinity of 3/(k!) ?

The sum from k=1 to infinity of 3/(k!) is converges

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sum from k=1 to infinity of 3/(k!)

k = 1 \sum \infty \frac{3}{k !}

converges

Solution steps

k = 1 \sum \infty \frac{3}{k !}

Apply the constant multiplication rule:

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

= 3 \cdot k = 1 \sum \infty \frac{1}{k !}

Apply Series Ratio Test:

converges

= 3 converges

= converges

n = 1 \sum \infty \frac{3}{2 + n}

n = 1 \sum \infty \frac{n !}{( 3 n ) !}

i = 0 \sum \infty i

n = 1 \sum \infty \frac{3}{n ^{3} + n}

n = 0 \sum \infty n - n

What is the sum from k=1 to infinity of 3/(k!) ?
The sum from k=1 to infinity of 3/(k!) is converges