Transcription of SEQUENCES AND SERIES
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SEQUENCES AND SERIES
VNatural numbers are the product of human spirit. DEDEKIND mathematics, the word, sequence is used in much thesame way as it is in ordinary English. When we say that acollection of objects is listed in a sequence , we usually meanthat the collection is ordered in such a way that it has anidentified first member, second member, third member andso on. For example, population of human beings or bacteriaat different times form a sequence . The amount of moneydeposited in a bank, over a number of years form a values of certain commodity occur in asequence. SEQUENCES have important applications in severalspheres of human , following specific patterns are called progressions. In previous class,we have studied about arithmetic progression ( ).
SEQUENCES AND SERIES 179 In the sequence of primes 2,3,5,7,…, we find that there is no formula for the nth prime. Such sequence can only be described by verbal description. In every sequence, we should not expect that its terms will necessarily be given by a specific formula. However , we expect a theoretical scheme or a rule for generating
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