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#### Resources tagged with Limits of Sequences similar to Summing Geometric Progressions:

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Broad Topics > Patterns, Sequences and Structure > Limits of Sequences ### 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? ### Continued Fractions I

##### Age 14 to 18

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