Answer
$122$
Work Step by Step
We expand and simplify the sum:
$\displaystyle \sum_{i=3}^{6}i(i+2)$
$3(3+2)+4(4+2)+5(5+2)+6(6+2)$
$=3\cdot 5+4\cdot 6+5\cdot 7+6\cdot 8$
$=15+24+35+48$
$=122$
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