How can visual patterns be used to prove sums of series?

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

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

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

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

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?