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Telescoping Series

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.

Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

OK! Now Prove It

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

Vanishing Point

Age 14 to 18 Challenge Level:

Try making some of the patterns by cutting up two squares of paper in contrasting colours.

How does this help you work out what proportion of the total area of the square is taken up by each colour?