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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Ratio Test:

converges

= \frac{1}{2} converges

= converges

\int x cos (mπ x) d x

\frac{\partial}{\partial x} (9 x e^{6 x y})

e^{5 (t)}

(3 x + 2 y + 1) d x - (3 x + 2 y - 1) d y = 0

f (t) = t - 2

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