June 9th, 2011, 11:47 AM  #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, 01:12 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,703 Thanks: 669  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, 02:32 PM  #3 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: induction
You could solve: 
June 10th, 2011, 05:34 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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