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 June 9th, 2011, 12:47 PM #1 Newbie   Joined: May 2011 Posts: 9 Thanks: 0 induction hi Can someone please help me I need to find a formula for the sum of the first n square numbers and then prove it by induction. This problem is actually up on google but im hoping someone can give me a better explaination and better working so i can actually understand Thanks
 June 9th, 2011, 02:12 PM #2 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 Re: induction The derivation from scratch is a little tricky. You can start by assuming it is a cubic polynomial in n. Therefore is has 4 coefficients. Calculate the value by hand for n = 1,2,3,4 and use this to determine these coefficients. Once you have the formula, use induction to prove it holds for all n.
 June 9th, 2011, 03:32 PM #3 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 Re: induction You could solve: $ax^3+bx^2+cx+d-[a(x-1)^3+b(x-1)^2+c(x-1)+d]= x^2$
 June 10th, 2011, 06:34 PM #4 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Perhaps the Faulhaber's formula should be sufficient where p = 2.

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