Generalise the sum of a GP by using derivatives to make the
coefficients into powers of the natural numbers.
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?
Is it true that a large integer m can be taken such that: 1 + 1/2 +
1/3 + ... +1/m > 100 ?