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.

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