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

y^{^{'}} = cos^{2} (y) ln (x)

\frac{\partial}{\partial x} (e^{5 x} sin (5 y))

\frac{x ^{2} - 1}{x ^{2} + x + 1}

y = - \frac{2}{x ^{2}}

2 sin (4 π (x + \frac{1}{8}))

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