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Problem 17 (2022 AMC 8)

AMC 8Normal

From module Arithmetic and Number Theory Basics

Problem

If nn is an even positive integer, the double factorial notation n!!n!! represents the product of all the even integers from 22 to nn. For example, 8!!=24688!! = 2 \cdot 4 \cdot 6 \cdot 8. What is the units digit of the following sum? 2!!+4!!+6!!++2018!!+2020!!+2022!!2!! + 4!! + 6!! + \dots + 2018!! + 2020!! + 2022!!

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