problem

Favourite

### Summing geometric progressions

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

problem
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Summing geometric progressions

Favourite

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

problem
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Slide

Favourite

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.

problem
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Squareness

Favourite

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?

problem
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Litov's Mean Value Theorem

Favourite

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

problem
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Diminishing Returns

Favourite

How much of the square is coloured blue? How will the pattern continue?

problem
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Climbing Powers

Favourite

$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

problem
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Approximating Pi

Favourite

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?

problem
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A Swiss sum

Can you use the given image to say something about the sum of an infinite series?

problem
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Small Steps

Two problems about infinite processes where smaller and smaller
steps are taken and you have to discover what happens in the limit.

problem
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Ruler

The interval 0 - 1 is marked into halves, quarters, eighths ...
etc. Vertical lines are drawn at these points, heights depending on
positions. What happens as this process goes on indefinitely?