Summation of series

  • A Swiss sum
    problem

    A swiss sum

    Age
    16 to 18
    Challenge level
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    Can you use the given image to say something about the sum of an infinite series?
  • Vanishing point
    problem

    Vanishing point

    Age
    14 to 18
    Challenge level
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    How can visual patterns be used to prove sums of series?
  • Summing geometric progressions
    problem

    Summing geometric progressions

    Age
    14 to 18
    Challenge level
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    Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

  • Double Trouble
    problem

    Double trouble

    Age
    14 to 16
    Challenge level
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    Simple additions can lead to intriguing results...
  • Speedy summations
    problem

    Speedy summations

    Age
    16 to 18
    Challenge level
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    Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

  • Seriesly
    problem

    Seriesly

    Age
    16 to 18
    Challenge level
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    Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!
  • Googol
    problem

    Googol

    Age
    16 to 18
    Challenge level
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    Find the smallest value for which a particular sequence is greater than a googol.
  • Clickety Click
    problem

    Clickety click

    Age
    16 to 18
    Challenge level
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    What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
  • Summing squares
    problem

    Summing squares

    Age
    14 to 16
    Challenge level
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    Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  • Succession in Randomia
    problem

    Succession in Randomia

    Age
    16 to 18
    Challenge level
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    By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?