For all integers n,
(n + 1)² = n² + 2n + 1 = (n²) + (2n + 1)
For n = 1,
(1 + 1)² = (1)² +2(1) + 1 = 1 + 3
For n = 2,
(2 + 1)² = (2)² +2(2) + 1 = 4 + 5
For n = 3,
(3 + 1)² = (3)² +2(3) + 1 = 9 + 7
For all integers n,
(n + 1)² = n² + 2n + 1.
→ (n + 1)²  n² = 2n + 1
For n = 1,
(2)²  (1)² = 2(1) +1 = 3
For n = 2,
(3)²  (2)² = 2(2) +1 = 5
For n = 3,
(4)²  (3)² = 2(3) +1 = 7
I forget what this method of proof is called or whether I really finished the proof, but I know I'm right. =]

Posted by Charley
on 20050514 09:37:07 