Limits of sequences

problem
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Slide

Age

16 to 18

Challenge level

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
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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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Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
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Diminishing Returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?
problem
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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...
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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?
problem
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Climbing Powers

Age

16 to 18

Challenge level

Does it make any difference how we write powers of powers?
problem

Small Steps

Age

16 to 18

Challenge level

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
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How Does Your Function Grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
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Little and Large

Age

16 to 18

Challenge level

A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?