Available online
Description
This programme takes the idea of a sequence of positive terms and develops it into the concepts of convergent and divergent series.
This programme takes the idea of a sequence of positive terms and develops it into the concepts of convergent and divergent series.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 3A; 1995 |
| First transmission date: | 1994 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:45 |
| Note: | A remake of the 1998 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 |
