The Sum of the First n Natural Numbers - Dynamic Geometric Proof

This applet gives a dynamic proof of the formula for the sum of the first n natural numbers.


Irina Boyadzhiev, 6 March 2013, Created with GeoGebra

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• See the general case - Arithmetic Series.

Irina's GeoGebra Applets

The Sum of Squares - dynamic proof

This applet gives a  dynamic proof of the formula for the sum of the squares of the first n natural numbers.  We start with three times the sum of the squares and rearrange the parts of one of the sums.

• Click on "Color the third column".
• Drag the slider to rearrange the parts of the third column.

The area of the formed rectangle equals three times the sum of the squares.

• Click on  Show the formulas  to see the result.

Irina Boyadzhiev, 13 February 2013, Created with GeoGebra

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Irina's GeoGebra Applets