Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Problem 7.4.8. Suppose (sn) is a sequence of positive numbers such that (*)- Sn+1 lim = L. Sn (a) Prove that if L < 1, then limn00 Sn = 0. Hint. Choose R with L < R < 1. By the previous problem, 3N such that if n > N, then Sn+1 < R. Let no > N be Sn fixed and show Sno+k < R*s ng. Conclude that lim-0 s no+k = 0 and let n = no + k. (b) Let c be a positive real number. Prove cn lim 0. %3D п!
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Transcribed Image Text:Problem 7.4.8. Suppose (sn) is a sequence of positive numbers such that (*)- Sn+1 lim = L. Sn (a) Prove that if L < 1, then limn00 Sn = 0. Hint. Choose R with L < R < 1. By the previous problem, 3N such that if n > N, then Sn+1 < R. Let no > N be Sn fixed and show Sno+k < R*s ng. Conclude that lim-0 s no+k = 0 and let n = no + k. (b) Let c be a positive real number. Prove cn lim 0. %3D п!
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