## Sequences and Series

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

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