Answer
$-20$
Work Step by Step
$\sum_{i=0}^{4} ((-1)^{i+1}i!)=((-1)^{0+1}0!)+((-1)^{1+1}1!)+((-1)^{2+1}2!)+((-1)^{3+1}3!)+((-1)^{4+1}4!)=(-1\cdot1)+(1\cdot1)+(-1\cdot2)+(1\cdot6)+(-1\cdot24)=-1+1-2+6-24=-20$
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