### Sums of Powers - A Festive Story

A story for students about adding powers of integers - with a festive twist.

### Slick Summing

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

### Summing Geometric Progressions

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

# Picture Story

##### Stage: 4 Challenge Level:

 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!