The S r ³  formula

Draw a 1 cm square

Now draw a 2 cm square to touch the first at a corner only

Finally draw a ‘border’ that produces a 3 cm square :  

Write in the dimensions of each sector of your diagram

This seems to indicate that :  

3 ² = ( 1 + 2 )² =  1² +  2² + 2 lots of ( ½.2² )

                           =  1.1² + 2. 2²

                           =   1³   +  2³

 i.e.                   1³   +  2³ = ( 1 + 2 )²

Draw some larger versions of this diagram, and see whether you have a general result. 

Use your formula to predict the value of 1³ + 2³ + 4³ + 5³ ... + 10³

Open the File as a Word Document

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Last modified: June 18, 2007