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Watch the video to see how Charlie works out the sum. Can you adapt his method?

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Summing Geometric Progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

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Picture Story

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

squares The picture illustrates the formula for the sum of the first six cube numbers:

$1^3 + 2^3 + 3^3 + ... + 6^3 = ( 1+ 2 + 3 + ... + 6)^2 $
Can you see which parts of the picture represent each part of the formula?

Could you draw a similar picture to represent the sum of the first seven cube numbers?

What about other sums of cubes?

Suggest a formula for the sum of the first $n$ cube numbers. Can you prove that your formula works, using diagrams and explanations? Send us your thoughts!

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.