Consider the following triangle

Prove that the relation hidden in the above triangle holds for any number of rows. Hint:find an expression for the sum of the ith row, and then prove its correctness.

  • $\begingroup$ expression for the sum: $i^3$? $\endgroup$
    – newzad
    Oct 17, 2013 at 19:00
  • $\begingroup$ expression for i row $\endgroup$
    – user101530
    Oct 17, 2013 at 19:32

1 Answer 1


i think you need something like this.

first number of $r$ th row is $r^2-r+1$ and the last one is $r^2+r-1$

so sum of $r$ th rows terms is $r\cdot\frac{(r^2-r+1)+(r^2+r-1)}{2}=r^3$


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