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An Odd Pyramid (Posted on 2003-10-14) Difficulty: 3 of 5
Consider the numerical pyramid below, formed by simply putting down the series of odd numbers into a pyramid.
         3   5
       7   9   11
    13  15  17   19
      . . .
Find a formula for the sum of the numbers in the nth row, and prove it.

See The Solution Submitted by DJ    
Rating: 4.1667 (12 votes)

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Solution Triangular numbers everywhere | Comment 6 of 21 |
The first number of the n-th row is twice the (n-1)th triangular number, plus one. The last number of the same row is twice the n-th triangular number, minus one. There are n numbers in the n-th row.

Thus, the sum of the numbers of the n-th row works out to be (n-1)n+1 plus n(n+1)-1, times n, which is n cubed.
  Posted by Federico Kereki on 2003-10-15 09:20:23

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