Skill |
Type |
Description |
Source |

16.1 Sequences and Series |
Workbook |
Check if a sequence of numbers is convergent + use the summation notation to specify series + recognise arithmetic and geometric series and find their sums |
HELM |

Limits of sequences |
Booklet |
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 sequen.. |
MathsCentre |

16.2 Infinite Series |
Workbook |
Use the alternating series test on infinite series + use the ratio test on infinite series + understand the terms absolute and conditional convergence |
HELM |

The sum of an infinte series |
Booklet |
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 se |
MathsCentre |

16.3 The binomial series |
Workbook |
Recognise and use the binomial series + state and use the binomial theorem + use the binomial series to obtain numerical approximations |
HELM |

Pascal's Triangle and the Binomial Theorem |
Booklet |
This unit explains how Pascal's triangle is constructed and then used to expand binomial expressions. It then introduces the binomial theorem |
MathsCentre |

16.4 Power Series |
Workbook |
Explain what a power series is + obtain the radius of convergence for a power series + explain what a general power series is.. |
HELM |

16.5 Maclaurin and Taylor Series |
Workbook |
Find the Maclaurin and Taylor series expansions of given functions + find Maclaurin expansions of functions by combining known power series together + find Maclaurin expansions by using differentiation and integration |
HELM |

Limits of functions |
Video - 17 mins |
This unit explains what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. A function which tends to a real limit as x tends to a given real number is also discussed |
MathTutor |

Limits of sequences |
Video - 18 mins |
This unit introduces finite and infinite sequences, and explains what it means for two sequences to be the same and what is meant by the n-th term of a sequence. The divergence of an infinite sequence to plus or minus infinity, or its convergence to a rea.. |
MathTutor |

The sum of an infinite series |
Video - 18 mins |
The partial sums of an infinite series form a new sequence. The limit of this new sequence (if it exists) defines the sum of the series. Two specific examples of infinite series that sum to e and pi respectively are described |
MathTutor |