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There's Even A Double Factorial!! (2022 AMC 8 P17)

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January 25, 2022
factorialAMC 82022 AMC 8

Problem Statement

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!!=2⋅4⋅6⋅88!! = 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!! + \cdots + 2018!! + 2020!! + 2022!!
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 8<span class='latex-bold'>(A)</span> ~0\qquad<span class='latex-bold'>(B)</span> ~2\qquad<span class='latex-bold'>(C)</span> ~4\qquad<span class='latex-bold'>(D)</span> ~6\qquad<span class='latex-bold'>(E)</span> ~8\qquad
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