video record
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Description
This programme takes the idea of a sequence of positive terms and develops it into the concepts of convergent and divergent series.
Metadata describing this Open University video programme
Module code and title: M203, Introduction to pure mathematics
Item code: M203; 3A; 1995
First transmission date: 1994
Published: 1995
Rights Statement: Rights owned or controlled by The Open University
Restrictions on use: This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OUDA web pages.
Duration: 00:24:45
Note: A remake of the 1988 programme
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Producer: Michael Peet
Contributors: David Brannan; Ian Harrison
Publisher: BBC Open University
Keyword(s): Convergent; Divergent; e (The number).; Exponential function; Partial sums; Sequences; Series
Subject terms: Calculus
Footage description: The prograrrme begins by using the analogy of a growing snake animation, to introduce the idea of convergence or divergence of a series as opposed to the sequence of terms of annual growths. Ian Harrison, in the role of practical investigator, considers the sequence. David Brannan, in the role of pure mathematician explains how to determine analytically that the series converges. Ian then introduces a trivial divergent series. David demonstrates analytically, how this series converges and points out that a convergent series must have arisen from a null sequence but that there are null sequences which lead to divergent Series. Finally Ian shows (with a computer animation) how an infinite number of functions, forming a series can be added up to give a graph of ex . The properties of ex are seen to be possessed by the curve that was produced.
Master spool number: DOU8016
Production number: FOUM477B
Videofinder number: 1735
Available to public: no