MathDB

2024 COMC B1

Source:

November 4, 2024

Comc

Problem Statement

For any positive integer number

k

, the factorial

k!

is defined as a product of all integers between

1

and

k

inclusive:

k!=k\times{(k-1)}\times\dots\times{1}

. Let

s(n)

denote the sum of the first

n

factorials, i.e.

s(n)=\underbrace{n\times{(n-1)}\times\dots\times{1}}_{n!}+\underbrace{(n-1)\times{(n-2)}\times\dots\times{1}}_{(n-1)!}+\cdots +\underbrace{2\times{1}}_{2!}+\underbrace{1}_{1!}

Find the remainder when

s(2024)

is divided by

8

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