What is the sum from n=1 to infinity of 1/((4n)!) ?

The sum from n=1 to infinity of 1/((4n)!) is converges

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sum from n=1 to infinity of 1/((4n)!)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty \frac{5}{0. 5 ^{n} - 2}

n = 0 \sum \infty \frac{2 ^{n}}{n ^{7}}

k = 2 \sum \infty (\frac{2}{3})^{3 k}

n = 1 \sum \infty n! e^{- 4 n}

What is the sum from n=1 to infinity of 1/((4n)!) ?
The sum from n=1 to infinity of 1/((4n)!) is converges