Summation of series

There are 31 NRICH Mathematical resources connected to Summation of series
Summing geometric progressions
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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
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Double trouble

Age
14 to 16
Challenge level
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Simple additions can lead to intriguing results...
Telescoping series
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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 $S_1, S_2, ... S_{r-1}$.
Picture Story
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Picture story

Age
14 to 16
Challenge level
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Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Clickety Click and all the Sixes
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Clickety click and all the sixes

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?
Picturing Square Numbers
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Picturing square numbers

Age
11 to 14
Challenge level
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Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Harmonically
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Harmonically

Age
16 to 18
Challenge level
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Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
Pocket money
problem
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Pocket money

Age
11 to 14
Challenge level
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Which of these pocket money systems would you rather have?
A Swiss sum
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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?