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

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

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

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

diverges

Solution steps

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

Simplify

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

Every infinite sum of a non-zero constant diverges

= \frac{1}{2} diverges

= diverges

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