Thread: Simplifying equations

hi all,
i wasnt sure what to put as the title of this thread. please see the attached file. im trying for hours how to simplify the equation on the LHS
cant see how its done
is it, quadratic equation? a simple trick? anything else?
any help, i would be thankful ! : )


thanks for reading this thread ; )

Originally Posted by matlabnoob

hi all,
i wasnt sure what to put as the title of this thread. please see the attached file. im trying for hours how to simplify the equation on the LHS
cant see how its done
is it, quadratic equation? a simple trick? anything else?
any help, i would be thankful ! : )


thanks for reading this thread ; )

Something that pops out at me immediately is

$\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$

Not sure how that fits in with proving or disproving the identity though.

Edit: Maybe they just threw that in for no reason. Unless there is a summation interpretation? Proving the identity is easy, as mr fantastic's post shows.

Originally Posted by matlabnoob

hi all,
i wasnt sure what to put as the title of this thread. please see the attached file. im trying for hours how to simplify the equation on the LHS
cant see how its done
is it, quadratic equation? a simple trick? anything else?
any help, i would be thankful ! : )


thanks for reading this thread ; )

Left Hand Side $\displaystyle = \frac{1}{3} \frac{n(n+1)(2n+1)}{n^3} = \frac{1}{3} \frac{n}{n} \frac{(n+1)}{n} \frac{(2n+1)}{n} = $ Right Hand Side.

aaah.. thanks ! that was simple : )