Can you solve it in 5 sec

Number Theory Level 2

If $n$ is an integer greater than or equals to 5, find the unit digit of $1!+2!+3!+\ldots+n!$ .

2 solutions

Adam Phúc Nguyễn
Aug 26, 2015

Try the first factorials:

$1!=1$ $2!=2$ $3!=6$ $4!=24$ $5!=120$ $6!=720 \ldots$

We can realize that because of $2\times 5=10$ , it forms an additional trailing zero. Therefore, we just add non-trailing-zero factorials:

$1+2+6+24=3\boxed{3}$

nice solution.

Shakil Ahmed - 5 years, 9 months ago

two1!+2!+3!+...+n! what is the last two

Bunneng Nath - 5 years ago

Shyam Gupta
Aug 26, 2015

5! and above has unit digit as 0 .. so we have to calculate for 1!+2!+3!+4! = 1+2+6+4= 3