Question

Express the following perfect squares in the pattern

n^2 = n(n+1)-n

3^2

4^2

5^2

6^2

Collected in the board: Square of numbers

Steven Zheng posted 5 hours ago

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

Steven Zheng posted 5 hours ago

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