Answer
$40$
Work Step by Step
Using the definition of the summation symbol, $\displaystyle\sum_{i=0}^4 i(i+1)
$ evaluates to
\begin{array}{l}
0(0+1)+1(1+1)+2(2+1)+3(3+1)+4(4+1)
\\=
0+2+6+12+20
\\=
40
.\end{array}
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