Question
Express the following perfect squares in the pattern
n^2 = n(n+1)-n
3^2
4^2
5^2
6^2
Answer
The pattern n^2 = n(n+1)-n is useful to derive the formula for the sum of consecutive squares 1^2+2^2+3^2+4^2+\dots
3^2 = 3\times4-3
4^2 = 4\times5-4
5^2 = 5\times6-5
6^2 = 6\times7-6