The product of any four consecutive positive | vedclass

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(C) Let the four consecutive positive integers be $n, (n+1), (n+2),$ and $(n+3)$.The product of these integers is $P = n(n+1)(n+2)(n+3)$.This expressi

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) Let the four consecutive positive integers be $n, (n+1), (n+2),$ and $(n+3)$.The product of these integers is $P = n(n+1)(n+2)(n+3)$.This expression is equivalent to $24 	imes \binom{n+3}{4}$.Since $\binom{n+3}{4}$ is always an integer,the product $P$ must be divisible by $24$.For example,if $n=1$,the product is $1 	imes 2 	imes 3 	imes 4 = 24$,which is divisible by $24$.If $n=2$,the product is $2 	imes 3 	imes 4 	imes 5 = 120$,which is $24 	imes 5$,also divisible by $24$.

The product of any four consecutive positive integers is always divisible by . . . . . . .

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