104lab7prep - MA104 Lab Report 7 Sequences and Series 1...

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MA104 Lab Report 7 – Sequences and Series1.Sequences (11.1)Asequencecan be defined by a function whose domain is the set of positive integers[ or the set of naturalnumbers,N={1,2,3, . . .}]and wheref(n) =angives thenth term of the sequence.The sequence isthen denoted by any of:{a1, a2, a3, . . . , an, . . .}{an}{an}n=1.The sequence is infinite, but note thatndoes not necessarily have to start at 1;e.g., both{an}n=0and{an}n=5represent a sequence.If a sequence{an}has a limitL[ denotedlimn→∞an=L,La unique finite value], then the sequence issaid toconverge;otherwise, the sequencediverges.Ifanis defined by the functionf(n),nZ,then iflimx→∞f(x) =L,we concludelimn→∞an=L.If, asnincreases, the value ofanincreases without bound, wewritelimn→∞an=and say the sequence{an}diverges to.

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