# Sequences & Series resources

### Teach Yourself (5)

Arithmetic and Geometric Progressions

This unit introduces sequences and series, and gives some simple examples
of each. It also explores particular types of sequence known as arithmetic
progressions (APs) and geometric progressions (GPs), and the corresponding
series.

Limits of sequences

In this unit, we recall what is meant by a simple sequence, and introduce
infinite sequences. We explain what it means for two sequences to be the same,
and what is meant by the n-th term of a sequence. We also investigate the
behaviour of infinite sequences, and see that they might tend to plus or minus
infinity, or to a real limit, or behave in some other way.

Pascal's triangle and the binomial theorem

This unit explains how Pascal's triangle is constructed and then used to expand binomial expressions.
It then introduces the binomial theorem.

Sigma notation

Sigma notation is a method used to write out a long sum in a concise way. In
this unit we look at ways of using sigma notation, and establish some useful
rules.

The sum of an infinite series

In this unit we see how finite and infinite series are obtained from finite and
infinite sequences. We explain how the partial sums of an infinite series form
a new sequence, and that the limit of this new sequence (if it exists) defines
the sum of the series. We also consider two specific examples of infinite
series that sum to e and pi respectively.

### Test Yourself (1)

Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

### Video (4)

Arithmetic and Geometric Progressions

This unit introduces sequences and series, and gives some simple examples
of each. It also explores particular types of sequence known as arithmetic
progressions (APs) and geometric progressions (GPs), and the corresponding series. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Limits of sequences

In this unit, we recall what is meant by a simple sequence, and introduce
infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequences, and see that they might tend to plus or minus infinity, or to a real limit, or behave in some other way. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Sigma notation

Sigma notation is a method used to write out a long sum in a concise way. In this unit we look at ways of using sigma notation, and establish some useful rules. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The sum of an infinite series

In this unit we see how finite and infinite series are obtained from finite and infinite sequences. We explain how the partial sums of an infinite series form
a new sequence, and that the limit of this new sequence (if it exists) defines
the sum of the series. We also consider two specific examples of infinite
series that sum to e and pi respectively. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.