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Factorials are fun

Source: 2019 AMC 10B #6, 12B #4

February 14, 2019
factorial2019 AMC 10B

Problem Statement

A positive integer nn satisfies the equation (n+1)!+(n+2)!=n!⋅440(n+1)! + (n+2)! = n! \cdot 440. What is the sum of the digits of nn?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>5\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>12\qquad<span class='latex-bold'>(E) </span>15
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