What is the sum from n=0 to infinity of 1/(2^nn!) ?

The sum from n=0 to infinity of 1/(2^nn!) is converges

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sum from n=0 to infinity of 1/(2^nn!)

n = 0 \sum \infty \frac{1}{2 ^{n} n !}

converges

Solution steps

n = 0 \sum \infty \frac{1}{2 ^{n} n !}

Apply Series Ratio Test:

converges

= converges

f (x) = \frac{( x ^{3} + 1 )}{( x ^{4} + 1 )}

x \to - 1 lim (\frac{x + 1}{x ^{2} - 1})

\int 2 4 - x^{2} d x

x \to π lim (\frac{( e ^{s i n (x)} - 1 )}{x - π})

x \to - \infty lim (7 x e^{x})

What is the sum from n=0 to infinity of 1/(2^nn!) ?
The sum from n=0 to infinity of 1/(2^nn!) is converges