SOLUTION: Prove using mathematical induction that for all n ≥ 1, 1 + 4 + 7 + · · · + (3n − 2) = n(3n − 1) /2

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Question 1189130: Prove using mathematical induction that for all n ≥ 1,
1 + 4 + 7 + · · · + (3n − 2) = n(3n − 1)
/2
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Show that the formula is true for n=1

For n=1, the formula says

1+=+%281%283%281%29-1%29%2F2%29
1+=+2%2F2
1+=+1 TRUE

(2) Show that, if the formula is true for some n, it is also true for n+1

We assume, as the formula says, that 1+4+7+...+(3n-2) is equal to %28n%283n-1%29%29%2F2 and add the next term (3%28n%2B1%29-2, or 3n%2B1) and show that the resulting expression is equal to %28%28n%2B1%29%283n%2B2%29%29%2F2

%28n%283n-1%29%29%2F2%2B3n%2B1
=%283n%5E2-n%29%2F2%2B%286n%2B2%29%2F2
=%283n%5E2%2B5n%2B2%29%2F2
=%28%28n%2B1%29%283n%2B2%29%29%2F2

The proof by induction is complete.