What is the sum from k=1 to infinity of (6k^5)/(k!) ?

The sum from k=1 to infinity of (6k^5)/(k!) is converges

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sum from k=1 to infinity of (6k^5)/(k!)

k = 1 \sum \infty \frac{6 k ^{5}}{k !}

converges

Solution steps

k = 1 \sum \infty \frac{6 k ^{5}}{k !}

Apply the constant multiplication rule:

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

= 6 \cdot k = 1 \sum \infty \frac{k ^{5}}{k !}

Apply Series Ratio Test:

converges

= 6 converges

= converges

m = 2 \sum \infty \frac{2}{3 ^{m}}

n = 4 \sum \infty \frac{1}{n ( n - 1 )}

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

n = 1 \sum \infty (\frac{e}{π})^{n + 1}

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

What is the sum from k=1 to infinity of (6k^5)/(k!) ?
The sum from k=1 to infinity of (6k^5)/(k!) is converges