SOLUTION: Use mathematical induction to prove the statement is true for all positive integers n. 6 + 12 + 18 + ... + 6n = 3n(n + 1)

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Question 1135717: Use mathematical induction to prove the statement is true for all positive integers n.
6 + 12 + 18 + ... + 6n = 3n(n + 1)
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

n=1: (3*1)*(1+1) = 6
n=2: (3*2)*(2+1) = 18 = 6 + 12


Assume true for n=k: n=k --> Sum = 3k(k+1)


Now let n=k+1:
Sum = (6+12+18+...+6k) + 6(k+1)
= 3k(k+1) + 6(k+1)
= 3(k+1)(k+2) <<<< factored out 3(k+1) from previous line
This concludes the proof.