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Series - A Level Maths Definition

Reviewed by: Mark Curtis

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What is a series?

In A Level Maths, a series refers to the sum of the terms in a sequence. For example, if a sequence is given by 4, 8, 12 and 16, then the series for this sequence is 4 + 8 + 12 + 16.

The notation S subscript n means the sum of the first n terms in a sequence. For the sequence above:

table row cell S subscript 1 end cell equals 4 row cell S subscript 2 end cell equals cell 4 plus 8 equals 12 end cell row cell S subscript 3 end cell equals cell 4 plus 8 plus 12 equals 24 end cell row cell S subscript 4 end cell equals cell 4 plus 8 plus 12 plus 16 equals 40 end cell end table

If a formula for the nth term of a sequence is known, then an alternative way to write a series is by using sigma notation, S subscript n equals sum from r equals 1 to n of straight f open parentheses r close parentheses.

Series resources to ace your exams

You can find out more about series by reading our revision notes. We also have exam questions on series to test your knowledge. For all of our A Level Maths resources (including past papers), click the link below.

Explore our A Level Maths revision resources

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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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