## Calculus: Early Transcendentals 8th Edition

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