Answer
$-4$
Work Step by Step
$\sum\limits_{k=1}^4(k-3)(k+2)=(1-3)(1+2)+(2-3)(2+2)+(3-3)(3+2)(4-3)(4+2)=(-2)3+(-1)4+0(5)+1(6)=-6+(-4)+0+6=-4$
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