The tens digit of the sum 1! + 4! + 7! + 10! | vedclass

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Question

(B) For any $n \geq 10$,the factorial $n!$ ends in at least two zeros (since $10! = 3628800$),meaning the tens digit of $n!$ is $0$ for all $n \geq 10

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) For any $n \geq 10$,the factorial $n!$ ends in at least two zeros (since $10! = 3628800$),meaning the tens digit of $n!$ is $0$ for all $n \geq 10$. Therefore,the tens digit of the sum $1! + 4! + 7! + 10! + 12! + 13! + 16! + 17!$ is the same as the tens digit of $1! + 4! + 7!$. Calculating the sum: $1! = 1$,$4! = 24$,$7! = 5040$. $1 + 24 + 5040 = 5065$. The tens digit is $6$. Since $6$ is divisible by $3$,the correct option is $B$.

The tens digit of the sum $1! + 4! + 7! + 10! + 12! + 13! + 16! + 17!$ is divisible by which of the following?

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