Prove or Disprove: Every oscillating sequence diverges.

Mathematics

Mark all the true statements about sequences of real numbers. Every sequence has a convergent subsequence. Every sequence has a monotonic subsequence. Every subsequence of a divergent sequence diverges. Every subsequence of a convergent sequence converges. Every sequence has a bounded subsequence.

Real Analysis Question:

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Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limft it diverges to infinity, state your answer as oo (without the quotation marks). If It diverges to negative Infinity, state your answer as -o0 If it diverges wfthout being infinity or negative infinity, state your answer as "DNE". 14 23 arctan((n) lim n+00 18t DNE Submit Question

Define a recursive sequence by a1 = 2 and an+1 = 1 − a2n. Either prove that (an) converges or prove that it diverges.

Algebra 1 STAAR Review Name: 1. Which graph does not represent y as a function of x? 1. II. impor C) III only Date: f A) I only B) II only E) I and II 2. Which expression is equivalent to 12x6y-4z² 3x²y-6z3 3. Which expression represents the nth term of this arithmetic sequence? -9, -5, -1, 3, 7, 9x8z5 A. 4x825 y-10 B. y-10 A. -9+(n-1)4 B. -9+ (n-1)(-4) 9x4y² C. D. 4x4,2 C. 7+ (n-1)4 7+(n-1)(-4) 4. A family will travel 350 miles from their house in order to reach Dallas, TX. Which inequality can be used to find all possible values of t, the time it will take this family to reach Dallas in hours, if they travel at an average speed of at leas miles per hour? (d = rt) A. t ≤ 350r B. t> C. t ≤ 350 350 D. t> 350r² 5. A print shop charges a fixed amount per photocopy and gives a 10% discount off the total cost of the photocopies. The total cost is a function of the number of photocopies made. What is the dependent quantity in this situation? A. The total number of photocopies made B. The…

Let {an} be a POSITIVE sequence. Which of the following statements must be true? Select all the correct answers. IF the sequence is bounded above, THEN it is convergent. IF the sequence is not bounded, THEN it is divergent. IF the sequence is convergent, THEN it is bounded. O IF the sequence is bounded, THEN it is eventually monotonic. O IF the sequence is non-decreasing, THEN it is convergent. O IF the sequence is non-increasing, THEN it is convergent. U

a. Find the equilibria of the sequence. b. Use the Stability Criterion to determine the stability of each equilibrium.