Answer
See below.
Work Step by Step
$S_k:3+4+5+...+(k+2)=\frac{k(k+5)}{2}$
$S_{k+1}:3+4+5+...+((k+1)+2)=\frac{(k+1)((k+1)+5)}{2}\\S_{k+1}:3+4+5+...+((k+3)=\frac{(k+1)(k+6)}{2}$
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