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Number Theory Level 2

Select the option that shows the relationship between 8 ! ! 8!! and ( 8 ! ) ! (8!)! .


Notations:

  • ! ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .

  • ! ! !! denotes the double factorial notation. For example, 10 ! ! = 10 × 8 × 6 × 4 × 2 10!!=10\times8\times6\times4\times2 .

8 ! ! = ( 8 ! ) ! 8!! = (8!)! None of these choices 8 ! ! > ( 8 ! ) ! 8!! > (8!)! 8 ! ! < ( 8 ! ) ! 8!! < (8!)!

Matin Naseri by Matin Naseri , 17, Afghanistan

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2 solutions

Matin Naseri
Feb 6, 2018

Double and multi factorials

(8!!) \text{(8!!)} = 2×4×6×8=384 \text{2×4×6×8=384}

(8!)!= \text{(8!)!=} (1×2×3×4×5×6×7×8=40320)!=(40320!=1×2×3×.....×40320) \text{(1×2×3×4×5×6×7×8=40320)!=(40320!=1×2×3×.....×40320)}

2×4×6×8=384 \text{2×4×6×8=384} < \boxed{<} 40320!=1×2×...×40320 \text{40320!=1×2×...×40320}

1 Helpful 0 Interesting 0 Brilliant 1 Confused

(8-2)(8-4)(8-6)<(8!)! 384<10^(10^5.225791225457473)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

This is not in LaTeX \LaTeX format.

And also this is not clearly.

But thank's for add a solution.

Matin Naseri - 3 years, 4 months ago

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