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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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