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Resources tagged with Limits of Sequences similar to Zooming in on the Squares:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Sequences, Functions and Graphs > Limits of Sequences

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Zooming in on the Squares

Stage: 2 and 3

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

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Litov's Mean Value Theorem

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

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Happy Numbers

Stage: 3 Challenge Level: Challenge Level:1

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

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Light Blue - Dark Blue

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the successive areas of light blue in these diagrams.