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Number Theory Level 3

Which is greater?

2018 ! or 2018 ! ! \large 2018! \text{ or } 2018!!

2018 ! = 2018 ! ! 2018! = 2018!! 2018 ! ! > 2018 ! 2018!! > 2018! 2018 ! > 2018 ! ! 2018! > 2018!!

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Jan 29, 2018

Relevant wiki: Double Factorials and Multifactorials

2018 ! ! = 2018 × 2016 × 2014 × … × 2 2018!! = 2018 \times 2016 \times 2014 \times \ldots \times 2

2018 ! = 2018 × 2017 × 2016 × … × 1 2018! = 2018 \times 2017 \times 2016 \times \ldots \times 1

2018 ! ! 2018!! contain just even integers, where 2018 ! 2018! contain both even and odd integers. Hence 2018 ! > 2018 ! ! 2018! > 2018!!

Note: If n n is a positive even integer, n ! ! = n × ( n − 2 ) × ⋯ × 4 × 2. n!!=n\times (n-2)\times \cdots\times 4\times 2.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Never knew about it before, thanks i guess

Aswin Ramesh - 3 years, 4 months ago

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