Parenthesis and Factorials

Algebra Level 2

If $2\times3\times\cdots \times n = 40320$ , what is $2 \div 3 \div \cdots \div n ?$

\frac 1{40320}

\frac 2{40320}

\frac 3{40320}

\frac 4{40320}

1 solution

Zach Abueg
Jul 1, 2017

$2 \times 3 \times 4 \times \cdots \times n = n! = 40320$

$\displaystyle \begin{aligned} 2 ÷ 3 ÷ 4 ÷ \cdots ÷ n & = \frac 23 \times \frac 14 \times \cdots \times \frac 1n \\ & = 4 \times \frac 12 \times \frac 13 \times \frac 14 \times \cdots \times \frac 1n \\ & = 4 \times \frac{1}{n!} \\ & = \boxed{\displaystyle \frac {4}{40320}} \end{aligned}$

Parenthesis and Factorials

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