Give me Five !!

Number Theory Level 2

$\begin{array}{c}1 1\times 3 \times 5 =1{\color{#3D99F6}5} \end{array} \\ 1\times 3 \times 5 \times 7 = 10{\color{#3D99F6} 5} \\ 1\times 3\times 5\times 7 \times 9 =94{\color{#3D99F6}5} \\ 1\times 3\times 5\times 7 \times 9 \times 11= 1039{\color{#3D99F6}5}$

Is it true that the unit digit of $n!!$ is always 5 if $n>3$ is an odd number ?

Inspiration

Notation: $!!$ denotes double factorial notation . For example : $7!! = 7\times 5\times 3\times 1$ and $4!! = 4\times 2$ .

Yes No

1 solution

Kellen Atkins
Jul 25, 2018

If n!! is an odd number and n > 3 then n!! = 5 * the product of odd numbers. Since the product of any odd numbers is an odd number and 5 * an odd number will end in 5 n!! will always end with a 5.

Give me Five !!

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