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.
(In reply to
re(2): solution by SilverKnight)
From SK's solution:
Like many other similar sequences... we can use the calculus of differences.
I love the way you approached this. I never thought of it. You are differentiating the 'function' until you get a straight line. This is done by calculating the slope between known points: (y1-y2)/(x1-x2). Since you know that (x1-x2) = 1, you just look at the difference in the values you've got. Thus enabling you to find the order of the function... Briliant!
re(3): solution (Well done)
