Week 7: A Reciprocal Sum
This is a bit of a longer problem – and could be expanded to start a nice investigation. The problem is given below:
Level of difficulty: Only HL
Syllabus knowledge required: This mixes a knowledge of graphs, ideas in formal proof and differentiation.
This is a good introduction to more formal mathematical techniques for finding upper/lower bounds for functions – and also in working with generalized functions. It would probably require longer than a usual starter. It would make a nice mini-investigation task and could be combined with using Desmos to draw some relevant graphs.
The pdf solution can be downloaded here.