Summation of series

  • Overarch 2
    problem

    Overarch 2

    Age
    16 to 18
    Challenge level
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    Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
  • 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?

  • Degree Ceremony
    problem

    Degree ceremony

    Age
    16 to 18
    Challenge level
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    Can you find the sum of the squared sine values?
  • Telescoping series
    problem

    Telescoping series

    Age
    16 to 18
    Challenge level
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    Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
  • 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.
  • 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.
  • Proof Sorter - Geometric Sequence
    interactivity

    Proof sorter - geometric sequence

    Age
    16 to 18
    Challenge level
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    Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
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