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There are **4** NRICH Mathematical resources connected to **Infinite series**, you may find related items under Calculus.

Problem
Primary curriculum
Secondary curriculum
### Diminishing Returns

How much of the square is coloured blue? How will the pattern continue?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Harmonically

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Circles Ad Infinitum

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Generally Geometric

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

Age 16 to 18

Challenge Level