A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
Can you work through these direct proofs, using our interactive
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
An arithmetic progression is shifted and shortened, but its sum remains the same...
A weekly challenge concerning the decay of medicines in the body.