How can visual patterns be used to prove sums of series?
Simple additions can lead to intriguing results...
Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Which of these pocket money systems would you rather have?
Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.