SOLUTION: use the principal mathematical induction to show that the statement is true for all natural numbers n. 9+18+27+...+9n= 9n(n+1)/2

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Question 438225: use the principal mathematical induction to show that the statement is true for all natural numbers n.
9+18+27+...+9n= 9n(n+1)/2
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
To prove a statement by mathematical induction we use three steps:
Step 1. We prove that the statement is true for n=1.
9=9%2A1%281%2B1%29%2F2 => 9=18%2F2 => 9=9.
Step 2. Assume that the statement is true for n=k.
9+18+27+...+9k = 9k(k+1)/2.
Step 3.We prove that the statement is true for n=k+1.
9+18+27+...+9k+9(k+1) = 9(k+1)(k+2)/2.
Substitute the assuming result in step 2 to the step 3 we have:
, thus
the statement is true.