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Resources tagged with Limits of Sequences similar to Weekly Challenge 48: Quorum-sensing:

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

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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?

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Continued Fractions I

Age 14 to 18

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

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Happy Numbers

Age 11 to 14 Challenge Level:

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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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?

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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?

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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?

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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...