Problem:
If is an even positive integer, the double factorial notation represents the product of all the even integers from to . For example:
What is the units digit of the following sum?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If we take for an even that is greater than or equal to , then is one of the numbers we multiply by. Since is a factor of , we know that the units digit of is , which means that it doesn't affect our result. This means it suffices to compute the units digit of , which is equivalent to:
The units digit therefore is .
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions