5040 is Product of Consecutive Numbers in Two Ways
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Theorem
- $5040 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 = 10 \times 9 \times 8 \times 7$
Proof
Follows from Factorial as Product of Two Factorials:
- $10! = 6! \times 7!$
and so:
- $\dfrac {10!} {6!} = 10 \times 9 \times 8 \times 7 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
Hence the result.
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5040$