You may also like

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?

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

OK! Now Prove It

Age 16 to 18 Challenge Level:

Are there any standard summations of series you can use to help you?

Once you have a conjecture, proof by induction is a possibility. You can read more about the technique in this article.

See also Natural Sum, Picture Story and Polynomial Equations.