12.4 Show lim sup(sn +tn) < lim sup s, +lim sup tn for bounded sequences (Sn) and (tn). Hint: First show sup{sn + tn : n > N} < sup{sn :n > N}+sup{tn :n > N}.

Q: Let (n) be a bounded sequence. (a) Prove that lim sup(x) = limm- (b) Prove that lim inf(x) = limm-…

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Q: Compute the limits of the sequences sin (n² – 3n + 7) n² +1 | 2n? +п -5 (b) b, (c) c, = n°e (а) а,…

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Q: 12. Suppose (an) is a Cauchy sequence, and that (bn) is a sequence satisfying lim,co lan - bn| = 0.…

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Q: 8.) Prove that lim (x₁) = 0 if and only if lin example to show that the the convergence of (Xn).…

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Q: Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b)…

A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

Q: 16. Show that if (s} and (ta} Cauchy sequence. Cauchy sequences, then {s + tn} is also are a.

A: Consider the provided question, We have to show that if {sn} and {tn} are Cauchy sequence then {sn +…

Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: how that every Cauchy sequence {pn} is bounded.

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Q: 1 a) Sn+1 = 3 – Sn 25, -35m b) Sn+1 Sn-1 9Sn c) Sn+1 S+1

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Q: 2 then E " Cn+1 converges. 3.11 limnr+m

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Q: Show that if (xn) and (yn) are bounded sequences, then lim sup(x, + Yn) < lim sup(x,) + lim sup(y,)

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Q: 7. Use the ratio test for sequences to prove that limn→∞ n¹/n² = : 1.

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Q: why cant an expert solve this? please help

A: Step 1:To prove this inequality, let's first understand what limsup and liminf mean.limsup (limit…

Q: Exercise 8. Let {an}-1 be a sequence such that an lim L+0. n-00 n Prove that {an}1 is not bounded.

A: Given that &lt;an&gt;is a sequence such that  limn→∞ann=L≠0 To prove: &lt;an&gt; is not bounded.

Q: 10 12 14 10 12 14 (b) Calculate dB at t = 2. dt 64 dollars per month (c) Explain what the number you…

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Q: 7

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Q: x[n]=(0,7)n.u[n] and h[n]=(0,9)n.u[n] to be y[n]=x[n]*h[n] Get the result of my processing…

A: Solution is in step 2

Q: 5 Let (sn) be a bounded sequence, and let k be a non number. onnegative real (a) Prove lim sup(ksn)…

A: Let Sn be a bounded sequence and let K be a non-negative real no. (a)  Let limn→∞Sup Sn=l Let K&gt;0…

Q: A sequence ₁,₂... is such that u, = -r-1 (i) (ii) n Show that Σ r=2 11+5 Hence find Σ r=8 =2_n+1 n!…

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Q: can you show your work on the paper so i can understand

A: To prove:liminfn→∞​yn​⋅(limsupn→∞​yn​xn​​)≤limsupn→∞​xn​ Given that  (xn) and (yn) are two positive…

Q: 4. If (x) is a sequence in an inner product space X such that the series converges, show that (sn)…

A: It is given that xj is a sequence in an inner product space X such that the series x1+x2+⋯…

Q: 32. Find the limit of the series: x (1+x) (+x) 1+x2 A) B) xx X+x C) (1+x D) (1+x) E) x

A: Given series is,

Q: 3.5.4) Show directly from the definition that of (xn) and (yn) Cauchy sequences, then cxntyn) and…

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Q: A momotone sequence converges if and only if it is bounded ylgn İhi

A: True

Q: 3. Prove that if (a, } and (b,} are Cauchy sequences of rational numbers satisfying lim (a, - b, = 0…

A: 3.

Q: +∞ W k=1 - k 7/4 x Ink 2 K²

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Q: +oo and inf{tn :n e N} > -∞, 11 (a) Show that if lim sn lim(sn + tn) = +o0. then (b) Show that if…

A: This question related to sequence from real analysis.

Q: 2) The purpose of this problem is to give you some practice with the most common application of The…

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Q: Question 1.3. (1) Show that 6 divides 7" +n³-3n² + 2n-1. for all integers n ≥ 0. C

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Q: 6. (a) A sequence {anneN is said to be bounded if there exists M > 0 such that an M for any n E N…

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Q: Q3/ Find out the convolution of two sequences given below: X(n) = x1(n) * x2(n) X1(n) = { 1, 0 , -3…

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Q: compute the partial sum when k=1 goes until infinity of ak. ak = 1/((k^2)+3k+2)

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