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## 'Diminishing Returns' printed from http://nrich.maths.org/

Take a look at the image below:

Work out what proportion of the image is coloured blue.

Try to provide a convincing explanation that your answer is
right.

Imagine continuing the pattern towards the centre of the square:

If this process could be continued forever, what proportion of the
image would be coloured blue?

Try to provide a convincing explanation that your answer is
right.

Below is a collection of images
created using repeating processes.
Choose a few of the images below, and work out what fraction of
the total is taken up by the five largest blue shapes.

Add your fractions to estimate the proportion of the total that is
coloured blue.

If each process could be continued for ever, what proportion of the
whole image would be coloured blue?

Try to provide convincing explanations that your answers
are right.

1 2

3 4

5 6

7 8

9