mathmath333
  • mathmath333
Prove
Linear Algebra
schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{Prove the number of squares in square of }\ n\times n \ \text{side}=\dfrac{n(n+1)(2n+1)}{6}\hspace{.33em}\\~\\ \end{align}}\)
mathmath333
  • mathmath333
|dw:1440712042217:dw|
freckles
  • freckles
can we do induction maybe?

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mathmath333
  • mathmath333
yea need short layman type proof
popitree
  • 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
mathmath333
  • mathmath333
nice easy
popitree
  • popitree
and consider one thing: the mentioned count is correct for perfect square, not for any rectangle

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