For which series monotone and bounded sequences theorem can be applied for the convergency? 2" I) (n+2)! n! A, n" II) 1.3.5.(2n– 1)(2n +1)| a, 2.4.6..(2n)(2n+2) III)

Q: +00 1 9n? – 18n + 8 n=1

A:

Q: (1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you…

A: Let's delve into a detailed step-by-step explanation: (a) Sequence ( (anbn) ) as ( n ) goes to…

Q: 1 3 Consider the sequence {an} where a1 = 2 and an+1 = An + 2 an 3 Show that v3 < an < 2 for all n.…

A:

Q: * 8 1-U 1=M 3 n = 2 (7) e n n³+1 = 20 Convergent / Divergent ? Conu. / Div. ?

A:

Q: Determine p and the radius of convergence of the sum Σ (n!)³²n² -x²n 2n (2n)! n=0

A:

Q: A sequence is defined by f (1) =5 and f (n)=3- f(n – 1) for nZE Which of the foikowing statements…

A:

Q: 4. Determine if the infinite series diverges or converges. a. E2 b. En1 (n+1)2-1 3n+1 4n+2 C. c. E…

A:

Q: 1 1 1 1 Ex. 1. (a) If an 1.2 2.3 3.4 п(п + 1) then show that {an} is a bounded monotonic increasing…

A:

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: Let (an) be a sequence such that (a)a, where a # 0. Show that la - a (3/4)a? lan-als and deduce that…

A: Given: an be a sequence such that an3→α3, with α≠0. To do: Show that…

Q: (Α True B False If the sequence {a}₁, is convergent, then the sequence {x} defined by…

A:

Q: • Let (*n) and (Yn) be bounded sequences. Show that lim inf x, + lim inf yn < lim inf(xn + Yn) < lim…

A: Recall that liminf(-xn)=-limsup(xn)

Q: n Determine whether the sequence Zn = (1+i)n answer (you may use any theorem or example proved in…

A:

Q: an= (-5)n an an = COS 4n+n3 3n+4" os(T) 8

A: The detailed solution with explanation is presented as the next step.

Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

A:

Q: Choose the correct answer. 1. The sequence (x) = (-n) is. a) Cauchy b) bounded e) divergent d)…

A: We have1) The sequence (xn)=(-n) is . . . . . . . . .Now we have take n=1 x1=-1put n=2x2=(-2) So, we…

Q: == 2.9 Let (an) be a sequence with limit a, and define bɲ = an+1 (n = 1, 2,...). Show that (bn) → a.

A: We know that  A sequence an converges to a limit L  if, for any positive real number epsilon there…

Q: A sequence is defined by f(1) = 3 and f(n) = 2. f(n –1) for n > 1. Which of the following statements…

A: Here given  f1=3,fn=2·fn-1

Q: +00 (-1)" n! n=1 O convergent O divergent

A:

Q: a1 = V6 V v6 a2 = 6 + az = V 6+ y6+ v6 /6+ võ a4 = 6+ V 6+ V6 + v6 a) Find a recursive formula for…

A: Follow next step

Q: 4 4 Write the sum 4 3 + ... using summation notation with n as the index of summation. (Using…

A:

Q: 10. For converging sequence (an), let f, (æ)= (ar+1-az )x*. k=1 Then, does function sequence…

A: We are given a sequence of functions,   We need to check whether it is uniformly convergent in…

Q: 1.5 Show that the series (a – 6)(a – 26) „3 + (a- b)(a- 26)(a- 35) | z+- 2! 3! 4! converges…

A:

Q: (h) l-(-1)" n+1 Converges or Diverges: Sum(If Converges):

A: We need to find whether ∑n=1∞1-(-1)nn+1 is convergent or not.

Q: n cos(n² + 3n + 4) ) n 1. The sequence {an}, where An has a convergent subsequence. n +1

A: