Lesson3.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF AGRICULTURE TECHNOLOGY JJ II J I J DocDoc I Back Close SCHOOL OF OPEN DISTANCE AND eLEARNING

Lesson3.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF...

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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close JOMO KENYATTA UNIVERSITY OF AGRICULTURE & TECHNOLOGY SCHOOL OF OPEN, DISTANCE AND eLEARNING P.O. Box 62000, 00200 Nairobi, Kenya E-mail: [email protected] SMA 2104 Mathematics for Sciences LAST REVISION ON May 10, 2013
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences This presentation is intended to covered within one week. The notes, examples and exercises should be supple- mented with a good textbook. Most of the exercises have solutions/answers appearing elsewhere and accessible by clicking the green Exercise tag. To move back to the same page click the same tag appearing at the end of the solu- tion/answer. Errors and omissions in these notes are entirely the re- sponsibility of the author who should only be contacted through the Department of Curricula & Delivery (SODeL) and suggested corrections may be e-mailed to [email protected] . JKUAT: Setting trends in higher Education, Research and Innovation 0
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences LESSON 3 Sequences and series Learning outcomes Upon completing this topic, you should be able to: Differentiate between a series and a sequence. Use Sigma notation in representing a series Understand the properties of arithmetic and geometric progressions Define an Arithmetic progression (A.P.) Obtain the formula for nth term and the first n terms of an A.P. Define a geometric progression (G.P.) JKUAT: Setting trends in higher Education, Research and Innovation 1
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences Obtain the formula for the nth term and the first n terms of a geometric series. Define convergence of series a G.P. series. JKUAT: Setting trends in higher Education, Research and Innovation 2
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences 3.1. Introduction Sets of numbers in which there is a definite rule for finding the next number in the set are called sequences . We often use the notation U n to denote the Uth term of the se- quence. e.g 5 , 10 , 15 , 20 ......... or 27 , 64 , 125 , 216 ..... or 1 , - 3 , 9 , - 27 ...... In the sequence 27 , 64 , 125 , 216 .... ... u 1 = 3 3 , u 2 = 4 3 , u 3 = 5 3 , u 4 = 6 3 and so the nth term can be given as u n = ( n + 2) 3 Hence a sequence may be defined as a set of terms in a defined order with a rule for obtaining each of the terms. Any number in the set is called a term When terms of a sequence are added together, a series is formed. A series having a finite number of terms is called a finite JKUAT: Setting trends in higher Education, Research and Innovation 3
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences series. e.g. 5+10+15+20+25+30+35+40 is a finite series . If a series does not stop but goes on indefinitely , it is called an infinite series. e.g. 1 + 1 4 + 1 16 + 1 64 + ............
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