Limits of sequences

  • Slide
    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.
  • Approximating Pi
    problem
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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?
  • Squareness
    problem
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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?
  • Diminishing Returns
    problem
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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?

  • Litov's Mean Value Theorem
    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...

  • Summing geometric progressions
    problem
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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?

  • Climbing Powers
    problem
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    Climbing Powers

    Age
    16 to 18
    Challenge level

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

  • Small Steps
    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.
  • Light Blue - Dark Blue
    problem

    Light Blue - Dark Blue

    Age
    7 to 11
    Challenge level
    Investigate the successive areas of light blue in these diagrams.
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