In this problem, you do NOT have to do formal proofs. Feel free to use phrases like, "We can see by inspection that sup A1 42." For each of the following sequences {an}, define the set An = {ar : k > n} and the numbers s, = sup A, and in = inf An as in the definition of lim sup and lim inf given in Session 25. Give an explicit formula in terms of n for Sn and in. (Your formula may be piecewise-defined.) Determine lim sup a,n and lim inf a, and use your results to determine whether {an} converges. (n-1)x (c) {0, 1,0, –1,0, 1,0, –1,...} (Note that this is the sequence {sin ("") })

In this problem, you do NOT have to do formal proofs. Feel free to use phrases like, "We can see by inspection that sup A1 42." For each of the following sequences {an}, define the set An = {ar : k > n} and the numbers s, = sup A, and in = inf An as in the definition of lim sup and lim inf given in Session 25. Give an explicit formula in terms of n for Sn and in. (Your formula may be piecewise-defined.) Determine lim sup a,n and lim inf a, and use your results to determine whether {an} converges. (n-1)x (c) {0, 1,0, –1,0, 1,0, –1,...} (Note that this is the sequence {sin ("") })

Name: In this problem, you do NOT have to do formal proofs. Feel free to us
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Description: In this problem, you do NOT have to do formal proofs. Feel free to use phrases like,"We can see by inspection that sup A1 = 42."For each of the following sequences {an}, define the set A, = {ar : k > n} and thenumbers s, = sup A, and i, = inf An as

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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