Sequences and Series AS

Circles Ad Infinitum

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Direct Logic

Stage: 5 Challenge Level: Challenge Level:1

Can you work through these direct proofs, using our interactive proof sorters?

Speedy Summations

Stage: 5 Challenge Level: Challenge Level:1

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Weekly Challenge 19: Prime Aps

Stage: 4 and 5 Short Challenge Level: Challenge Level:1

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Weekly Challenge 14: Mad Robot

Stage: 5 Short Challenge Level: Challenge Level:1

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Weekly Challenge 6: AP Train

Stage: 5 Short Challenge Level: Challenge Level:1

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Weekly Challenge 32: Medicine Half Life

Stage: 4 and 5 Challenge Level: Challenge Level:1

A weekly challenge concerning the decay of medicines in the body.