SOLUTION: Use mathematical induction to prove the statement is true for all positive integers n. 8+16+24+...+8n=4n(n+1)

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Question 1036224: Use mathematical induction to prove the statement is true for all positive integers n.
8+16+24+...+8n=4n(n+1)
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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Use mathematical induction to prove the statement is true for all positive integers n.
8+16+24+...+8n=4n(n+1)
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Hey, take the factor 8 out of the parentheses, and you will get

8*(1 + 2 + 3 + . . . + n) = .

It is well known fact that

1 + 2 + 3 + . . . + n =

proven many times by many methods, including the method of the mathematical induction.

See the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions,
    - Mathematical induction and arithmetic progressions
in this site.


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