Find the remainder when $1! + 2! + 3! + 4! + 5! + . . . . + 100!$ is divided by 24 .

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Solution

We have to find the remainder when $1! + 2! + 3! + \dots \dots . . + 100!$ is divided by $24$ .

$1! + 2! + 3! + \dots \dots . + 100! = 1 + 2 + 6 + 24 +$ (multiply of $24$ ) then when it is divided

by $24$ , we get remainder as $1 + 2 + 6 = 9$ .

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