It displays two graphs which plot the value and sum of the first twenty terms of a geometric series with first term 0.8 and a changeable common ratio. The resource also includes how a proof of the formulae for the sum to infinity can be deduced from the sum of the first n terms.As well as a demonstration of the effect of changing the common ratio for a geometric series for |r| < 1. The terms of a geometric progression, where |r| < 1 and given as a decimal or common fraction, can also be generated. It displays two graphs which plot the value and sum of the first twenty terms of a geometric series with first term 0.8 and a changeable common ratio, for |r| ≥ 1. The second interactive sheet demonstrates the effect of changing the common ratio for a geometric series. The first sheet generates the terms of a geometric progression, for |r| ≥ 1, and the value of a further term. New sequences can be generated each time by the click of a button. This interactive excel file from The Virtual Textbook covers geometric series and progressions. Quality Assured Category: Mathematics Publisher: The Virtual Textbook The sigma notation resource introduces the method of representing long sums, as well as asking students to expand a sum given in sigma notation, to write an explicit sum in sigma notation where there is an obvious pattern to the individual terms and to use rules to manipulate sums expressed in sigma notation. Limits of sequences covers the formula for the nth term of sequence whether a sequence tends to positive or negative infinity whether it tend to a real limit or diverges nad the notation for the limit of a sequence. The sum of an infinite series allows students to recognise the difference between a sequence and a series write down the sequence of partial sums of an infintie series and determine (in simple cases) whether an infinite series has a sum. Each topic includes a selection of questions to be completed, for which answers are provided. Students wishing to review, and consolidate, their knowledge and understanding of sequences will find them useful. Each contain comprehensive notes, with clear descriptions, together with relevant diagrams and examples. There are three resources in this mathscentre collection. Quality Assured Category: Mathematics Publisher: Mathcentre
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