Answer
See explanations.
Work Step by Step
Step 1. Check the statement is true for $n=1$, $LHS=6$, $RHS=3(1)(1+1)=6=LHS$
Step 2. Assume the formula is true for $n=k$, we have $6+12+18+...+6k=3k(k+1)$
Step 3. For $n=k+1$, $LHS=6+12+18+...+6k+6(k+1)=3k(k+1)+6(k+1)=3(k+1)(k+2)$ and $RHS=3(k+1)(k+1+1)=3(k+1)(k+2)=LHS$
Step 4. Thus, through mathematical induction, we have proved that the statement is true for every positive integer $n$.
