Summation of series

There are 31 NRICH Mathematical resources connected to 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?