Summation of series

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Harmonically

Age

16 to 18

Challenge level

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
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Pocket Money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?
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Picturing Square Numbers

Age

11 to 14

Challenge level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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Double Trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
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Picture Story

Age

14 to 16

Challenge level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
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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?
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The Root of the Problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
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Clickety Click and All the Sixes

Age

16 to 18

Challenge level

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
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Telescoping Series

Age

16 to 18

Challenge level

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
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Summats Clear

Age

16 to 18

Challenge level

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.