## mathmath333 one year ago Prove

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{Prove the number of squares in square of }\ n\times n \ \text{side}=\dfrac{n(n+1)(2n+1)}{6}\hspace{.33em}\\~\\ \end{align}}

2. mathmath333

|dw:1440712042217:dw|

3. freckles

can we do induction maybe?

4. mathmath333

yea need short layman type proof

5. popitree

how many squares with side = 1 == n^2 how many squares with side = 2 == (n-1)^2 .... how many squares with side = n-1 == 2^2 how many squares with side = n == 1 = 1^2 so total squares = 1 + 2^2 + 3^2...+n^2 sum of square of first n natural numbers now i believe you can do

6. mathmath333

nice easy

7. popitree

and consider one thing: the mentioned count is correct for perfect square, not for any rectangle