Mark all of the sequences that are bounded. {} {In(n)}1 O{cos(n)}1 In V n+1, O {e"}_1 n=1 n=1

Q: Determine the limit of the sequence a, = [In(n + 1)-in(n)] 1 e 1 in 2 1 4 e Divergent N O

A: Topic = Limits

Q: Consider the sequence In+1 n = 0, 1, 2,... (a) Show that this sequence is generated by Newton's…

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Q: 2. For n E N, let fn(2) - converges uniformly on [0, 1]? nx +sin(nx?) n 1 (a) Show that the sequence…

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Q: n cos(n) V1+4n2 (an) at n→∞o or prove that the limit does not exist: (b) In(1+2n²) - 2 ln(1 + n)

A: 7) a) an=ncos(pi n) /sqrt(1+4n2)b) an)-2ln(1+n)

Q: 3. Express 0.7 + 0.007 + 0.00007 + ... using sigma notation. A) Σ0.7)1001 B ) Σο0.7)100" C)…

A: By using the formula of geometric progression and Arithmetic progression we can solve this question.

Q: Find the limit superior and limit inferior of following sequences sin() • an = n n = 1, 2, 3, .. if…

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Q: Let f = C(R/Z; C), and for n= 0,1,2,... define 2/₁₁ (2) cos(2x)da; by = 2(a) sin(2xnx)da. 0,1] Show…

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Q: 2.2.1. Prove that each of the following sequences converges to zero. write a) xn =…

A: We have to show that the following sequences  converge to zero.

Q: Exercise 3: Let n E N withn > 1. Show that (1 +x)" > 1+ nx for all x < 0.

A: Given that

Q: 13. (a) Express each of following sum in sigma notation 1 a) 1 + 2 + 113 +... + 1 20 b)…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: In(1+2e") d) an n

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 30 (a) Find the sum of 2k+1. k=2 (b) Show that if Re z < 0, then Je| <1 and find the sum of ) ek*.…

A: i have given the formulas that i have used in the step where i have used them

Q: 1. Let {f} be a sequence of integrable functions on E, i.e. fn L¹(E) Vn N. Suppose {fn} → f…

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Q: Mark each sequence {n} having the property that In In (-1)"n n+1 In |xn = (-1)" In = {cos(nn/3)} 1…

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Q: Mark all of the sequences that are bounded. KA O{n¹/¹}=1 n=1 {sin(n²)}=1 In(n) [ n√n=1 In ² n² + 1…

A: To check whether given sequences are bounded or not. i.e., all terms of sequences are both bounded…

Q: For the sequence an = n cos n n² +1

A: given a sequence

Q: Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn…

A: The objective of the question is to analyze the given sequences in terms of monotonicity,…

Q: Let Hn = the sum from i= 1 to n of 1/ifor any n ≥ 1. Prove or disprove that for any n ≥ 1H2n ≥n/4.

A: So, Hn looks like,             We will use mathematical induction to show that,…

Q: Use sigma notation to write the sum.

A: ​[2(1+n3​)2](n3​)+⋯+[2(1+n3n​)2](n3​)=i=1∑n​[2(1+n3i​)2](n3​)​Explanation:Step…