Problem of the Week

Problem C

How It Ends

The product of the positive integers 1 to 4 is $4\times 3\times 2\times 1 =24$ and can be written in an abbreviated form as $$4!$$. We say “4 factorial”. So $$4!=24$$.
The product of the positive integers 1 to 16 is $16\times 15\times 14\times\cdots\times 3\times 2\times 1$ and can be written in an abbreviated form as $$16!$$. We say “16 factorial”.
The $$\cdots$$ represents the product of all the missing integers between 14 and 3.
In general, the product of the positive integers 1 to $$n$$ is $$n!$$. Note that $$1!=1$$. Determine the tens digit and units (ones) digit of the sum $1!+2!+3!+ \cdots +2019!+2020!+2021!$

Themes: Algebra, Number Sense