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