4. Suppose that lim r, = 0. If (yn) is a bounded sequence, prove that lim In Yn = 0.

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Q: 22: Establish the divergence of the sequence x, =(-1)"

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Q: Define the sequence {Sn} by Sn= [ 1 / (2)(1) ] + [ 1 / (3)(2) ] +   .............  + [ 1 / (n+1)(n)…

A: The nth term of the partial sum is given by

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A: Step:-1 Limit of a sequence:- Let f(n) be a sequence of real numbers and let l be a real number then…

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Q: Additional Problem 2: Prove that the quantity tz =1+ ++...+!- In(k) is a monotone decreasing…

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Q: Show that if lim 0 and E- b, converges then Ena, a, converges too.

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Q: Let ₁1 and In+1 = limit. 1 for n N. Show that this sequence is convergent and find its In + 2

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Q: 3. Show that if x1 = 1 and if In+1 Van + 2 for n E N, then the sequence (xn) is monotone and…

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Q: 4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0 %3D

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Q: Prove that the sequence is monotone and bounded. Then find its limit. s1 = 5 and sn+1 = V4sn +1 for…

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Q: 3. Use the definition of limits of sequence to give a formal proof of lim (Vn+1- yn) = 0. n00

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Q: If {xn} is a bounded sequence on R. Prove: lim n→+∞

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Q: Find the limit of the sequence whose terms are given by 4.9 1 Cos In =

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Q: 28. yn = ne/n

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A: The given sequence is,

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Q: 4. Let (#1, y1) = (0,0) and let (n+1, Yn+1} = (2+ yn, 3 – Tn) for n > 1. Prove that (Cn, Yn) is a…

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Q: Determine the one dimensional DFT for the following sequence x(n)= { 0,\ / 7 / l }

A: Sol:- Given Sequence :- xn=0,1,7,1One Dimension DFT  is given by Xw=11111-j-1j1-11-11j-1-j0171

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Q: Find a sequence X, Such that X, does not converge (to any XE R) and Y, does converge to 0 where Y,…

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Q: Use Theorem 1 from Section 10.1 to determine the limit of the sequence, or state that the sequence…

A: Solve the following