Search by Topic

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 4 results

Broad Topics > Pre-Calculus and Calculus > Infinite series

problem icon

Harmonically

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

problem icon

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?

problem icon

Diminishing Returns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

problem icon

Generally Geometric

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

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.