Summation of series

  • 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?

  • 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!

  • 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.

  • 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?

  • OK! Now prove it
    problem

    Ok! Now Prove It

    Age
    16 to 18
    Challenge level
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    Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

  • Sum the Series
    article

    Sum the Series

    This article by Alex Goodwin, age 18 of Madras College, St Andrews describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n terms.
  • Powerful properties
    article

    Powerful Properties

    Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.
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