1. ## AP

How to prove that sum of 'n' odd integers is n^2 graphically???????

i need immediate help for my project..

2. Originally Posted by anandcu3
How to prove that sum of 'n' odd integers is n^2 graphically???????

i need immediate help for my project..
HI

i am not sure what u meant by graphically ...

But

Odd integers has a general term of $\displaystyle 2r-1$

hence $\displaystyle \sum^{n}_{r=1}(2r-1)=2\sum^{n}_{r=1}r-\sum^{n}_{r=1}1$

$\displaystyle =2(\frac{1}{2})n(n+1)-n$

$\displaystyle =n^2+n-n$

$\displaystyle =n^2$

3. Originally Posted by anandcu3
How to prove that sum of 'n' odd integers is n^2 graphically???????

i need immediate help for my project..
By arranging, say $\displaystyle 5^2$ dots into a square. In the bottom left corner, draw a line separating the dot in the corner from the one above it and the one to the right (the line will be a sort of upside down L shape).

Then draw a similar bigger line separating off the 2x2 block in that same bottom left corner from the rest of the dots above it and to the right.

Then do the same for the next bigger square, the 3x3 one. And so on.

You will notice that the square will be divided into upside-down-L-shaped sections, with one dot, three dots, five dots, 7 dots ... and so on.

4. Originally Posted by anandcu3
how to prove that sum of 'n' odd integers is n^2 graphically???????
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1 + 3 + 5 + 7 + 9

5. ## thanks

Thanks for the help..
westwood