Resources tagged with: Limits of Sequences

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There are 6 results

Broad Topics > Patterns, Sequences and Structure > Limits of Sequences

Litov's Mean Value Theorem

Age 11 to 14
Challenge Level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Archimedes and Numerical Roots

Age 14 to 16
Challenge Level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Zooming in on the Squares

Age 7 to 14

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?

Continued Fractions I

Age 14 to 18

An article introducing continued fractions with some simple puzzles for the reader.

Approximating Pi

Age 14 to 18
Challenge Level

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Summing Geometric Progressions

Age 14 to 18
Challenge Level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?