9. Two recursive sequences u, and v, are defined by 1 Uo = 9, Un+1 =5Un – 3 2 Vn = Un + 6 i) Show that v, is a geometric sequence with common ratio r = and vo = 15 %3D ii) Calculate Sn = Ek=o Vk In terms of n iii) Hence or otherwise, find Tn = EX=0 Uk In terms of n.

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

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Q: II. Prove if X and Y are the sequence of real number and converges to x a real number then product…

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A: According to this question, we know that

Q: 7) Show that if a, > 0, and Lim na, 0, then the series а, + a, + а, + a, + ... diverges.,

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Q: Prove that there is no hooked Skolem sequence of order n= 8.

A: To Prove - Prove that there is no hooked Skolem sequence of order n = 8.         Theorem used - A…

Q: The formula for calculating the sum of all natural integers from 1 to n is well-known: n² + n 2 Sn =…

A: Given:  Sn= 1+2+3+.......................+n = n2+n2and,Qn=1.1+2.2+3.3+...............+n.n=n33+n22+n6

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A: Option d is correct.

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Q: Find the limit of the sequence 14n2 – 8n – 7 1 18 – n + 7n² . - - - n=1

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Q: 4. For the sequences L (X1, X2, x3) = (50, 40, 10) %3D and (y1, y2. y3) = (3, 1,5) %3D 3 The max of…

A: Given:x1,x2,x3= 50,40,10and y1,y2,y3=3,1,5This means x1,=50 x2,=40 x3=10and y1,3 y2,=1…

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Q: Suppose Sanx",Σ bnan converges for all x in (-1,1). Σana" = Σbnan in a subset E of (-1,1) implies…

A: It is given that,  ∑anxn and ∑bnxn are convergent for all x in (-1, 1). Then,  ∑anxn = ∑bnxn in a…

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Q: Find an explicit formula for a sequence ao, a1, a2, a3, . . . that satisfies — 24. (Hint: ат Cr" +…

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Q: Suppose that a sequence is defined a=-3, + 10 n-1 List the first four tor mc of th

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Q: Suppose that the sn satisfies both limn→∞ s2n = 2 and limn→∞ s2n+1 = 2. (That is, the sequence given…

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Q: 8. Suppose that họ, h1, h2, . . . is a sequence défihed as follows: ho = 1, h = 2, h2 = 3, h =…

A: I have given the proof in details

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Q: oll Show that sequence {n} n = 1, where .... 1/1₂ 0₂0₂...) converges 1/1,0,0 :) 9 9... 1/ng...) in…

A: We have to show that the sequence xnn≥1 defined by ; xn = 1, 12, ..., 1n, 0, 0,...  converges to  x…

Q: (a) Let {n} be a sequence such that there exist A> 0 and c € (0, 1) for which n+1- n ≤ Ac" for all…

A: As per the policy, we are solving first question. Please repost the question and specify which…

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Q: The sequence 7² – 1 - V n² +n converges to – 2 Select one: 23 True O False

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A: @solution::::

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Q: Show directly from definitions that if sn and tn are sequences so that limn→∞sn = 5 and limn→∞tn =…

A: We have two sequences sn and tn such that limn→∞ sn=5 and limn→∞ tn=∞. We have to show that limn→∞…

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Q: 5. Find the limit of the sequence 3. an ), n = 1,2, 3, --. 3JT

A: Explained below

Q: п+1 2n +1 dn + Vn² · 6n+1. 2n ||

A: Note some standard results of limit: limn→∞ 1+1nn=e limn→∞ n1n=1 Suppose xn and yn are two…

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A: Solution :-    The given sequence is              an =   1/( n2 + n + 1 )     ;  n belong to N .…

Q: 3. Let 2n2 + 3 |an| < for alln E N. n3 + 5n2 + 3n +1 Show (using definition of Cauchy Sequence) that…

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Q: 1. Show that the sequence fh3, whore fnex) = tan nx , x7o is uniprmly on ony Interval Ca,6], a> o…

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

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Q: Does a(n)= n^2sin(3/n^2) converge?  If so, to where

A: The given question can be solved as shown in step2.

Q: In(n+19)165 Lin(33+88 n )132 The sequence is O and its limit is n=1 nit Answer divergent convergent

A: Given sequence is lnn+19165ln33+88n132n=1∞. Let, xn=lnn+19165ln33+88n132, ∀n∈ℕ.

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A: a) We have to pick 3 positions for three 1's. Then the positions of 0's will be fixed.  From 12…

Q: (a) Let {n} be a sequence such that there exist A> 0 and c € (0, 1) for which n+1-In ≤ Ac" for all…

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Q: 7) Show that if a, > 0, and Lim na, +0, then the series aj + az + az + a4 + diverges.,

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Q: portion

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