Answer
See below.
Work Step by Step
$S_1:3=\frac{1(1+5)}{2}=\frac{6}{2}$, thus this is true
$S_2:3+4=7=\frac{2(2+5)}{2}=\frac{14}{2}$, thus this is true
$S_3:3+4+5=12=\frac{3(3+5)}{2}=\frac{24}{2}$, thus this is true
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