Sequences are everywhere in mathematics! In these problems you can explore some sequences, learn how to represent them, and how to calculate sums of series.
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?