SOLUTION: In mathematics, n! means the product of the numbers from 1 to n. For example, 3! = 1 × 2 × 3. Determine the one’s digit of the sum 1! + 2! + 3! + · · · + 18! + 19! + 20! a 0

Algebra ->  Sequences-and-series -> SOLUTION: In mathematics, n! means the product of the numbers from 1 to n. For example, 3! = 1 × 2 × 3. Determine the one’s digit of the sum 1! + 2! + 3! + · · · + 18! + 19! + 20! a 0      Log On


   

Question 307267: In mathematics, n! means the product of the numbers from 1 to n.
For example, 3! = 1 × 2 × 3. Determine the one’s digit of the sum
1! + 2! + 3! + · · · + 18! + 19! + 20!
a 0 b 3 c 5 d 7 e 9
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1! = 1
2! = 1! * 2 = 1 * 2 = 2
3! = 2! * 3 = 2 * 3 = 6
4! = 3! * 4 = 6 * 4 = 24
5! = 4! * 5 = 24 * 5 = 720
6! = 5! * 6 = 720 * 6 = 4320
7! = 6! * 7 = 4320 * 7 = 30240

Once the units digit becomes 0, it will remain 0 forever because any number times 0 will always equal 0.

The units digit of the sum will remain what it is after you reach 4!.

1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

The units digit of the sum of the factorials is 3 and will remain 3 forever.

That would be selection B.