This picture shows the first 4 triangle numbers: 1, 3, 6 and 10 and how you can fit 2 identical copies of a triangle together to form a rectangle.
Can you use it to find the number of dots in the […]
What patterns do you notice in this table?
Continue the patterns to fill the empty squares.
Write a list describing all the patterns that you see.
What do you notice about the numbers on squares of the same colour?
Would the patterns […]
Practical activities like shaking hands, taking 2 books from a shelf and drawing the mystic rose pattern lead to understanding how to find the sum of a series and how and why different methods lead to the same result. These activities give learners the opportunity to develop logical thinking, and problem solving […]
Multiply out these expressions:
What do you notice?
Does this pattern continue?
Can you prove it?
What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?
Why do we get a formula for all values of r except r = 1?
The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .
Try this with other numbers. What do you notice? Can you explain why? Can you find different ways to explain (and prove) the result that you noticed. You might use what you […]