Discrete Structure lecture_16

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 16SEQUENCEKHAWAJA TARIQ MAHMOODLecture # 16SEQUENCESEQUENCE:A sequence is just a list of elements usually written in a row.EXAMPLES:1.1, 2,3, 4,5,...2.4,8,12,16, 20,...3.1, 1,1, 1,...NOTE:The symbol is called ellipsis, and reads and so forthFORMAL DEFINITION:A sequence is a function whose domain is the set of integers greater than or equal to a particularinteger n0 . Usually this set is the set of Natural numbers {1, 2, 3 } or the set of whole numbers{0, 1, 2, 3 }.NOTATION:We use the notation an to denote the image of the integer n, and call it a term of the sequence.Thus a1, a2, a3, a4 , an, represent the terms of a sequence defined on the set of naturalnumbers N.Note that a sequence is described by listing the terms of the sequence in order of increasingsubscripts.FINDING TERMS OF A SEQUENCE GIVEN BY AN EXPLICITFORMULA:An explicit formula or general formula for a sequence is a rule that shows how the values of akdepends on k.EXAMPLE:Define a sequence a1, a2, a3 by the explicit formulaKhawaja Tariq Mahmood.Page 2Lecture # 16ak SEQUENCEkfor all integers k 1k 1SOLUTION:The first four terms of the sequence are:a1 1111 2a2 222 1 3a3 333 1 4a4 444 1 5EXAMPLE:Write the first four terms of the sequence defined by the formula b j 1 2 j for all integers j 0SOLUT

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