¶ 2022 AMC8 Problem 17
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:
The values of for the first few terms in the sum are shown in the table below:
The last two rows of the table show that for even numbers , the number will appear as one of the factors in , and hence the units digit of will be . Thus the units digit of the sum given in the problem is the same as the units digit of , so the answer is .
If is an odd positive integer, then represents the product of all the odd integers from . For example, .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions