(6) Lettan }n=obe a sequence. Prove that if an n=o is decreasing and not bounded below, then it is divergent to -o. Do a proof directly from the definition of these concepts.
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- A sequence is bounded if it is bounded above and below. Suppose that {an} is bounded and that {bn}---->0. Prove that {anbn}---->0Prove Theorem 10.2 for bounded decreasing sequences. Theorem10.2 is All bounded monotone sequence converge. please show clear,thanksHow do I show that the {Xn} be a convergent monotone sequence. Suppose there exist a k be an element on natural number such that Lim Xn=Xk. Show that Xn = Xk for all n>=K?
- *You cannot use any theorems about convergent sequences* Using the definition of a convergent sequence, prove:Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an = 2 −(1/ 4n )A sequence is defined by tn=tn−1+3n and t1=1 Determine the fourth term in this sequence
- "If a sequence is convergent then it is bounded and monotone." Give an example and explain why this statement is false.Use Theorem Bounded monotonic Sequences to show that the sequence with the given nth term converges and use a graphing utility to graph the first 10 terms of the sequence and find its limit.