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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.
           1
         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 Solution | Comment 4 of 21 |
n²*n. n² will always get you the mean of the row. The mean of a set times the number of elements in the set gets the sum of all the numbers in the set. Take the fourth row. 4² is 16. 13+15+17+19=4²*4=64. If you check any other row, this solution will work.
  Posted by ethan on 2003-10-14 16:27:24
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