Provide a detailed response to the followina a) State th b) Give the -N definihon of...
(a) Prove explicitly that the sequence (n2 -ncos(n))0 is eventually monotone by finding a number N E N such that the subsequence (n2-n cos(n))n-N İs monotone. (b) Does the monotone convergence theorem allow us to conclude that this sequence converges? Explain. (a) Prove explicitly that the sequence (n2 -ncos(n))0 is eventually monotone by finding a number N E N such that the subsequence (n2-n cos(n))n-N İs monotone. (b) Does the monotone convergence theorem allow us to conclude that this sequence...
2. (a) Let 11 = 0 and Zn+1=2r" +1 for all n E N. In +2 i. Find 2, , and ii. Prove that (r converges and find the value of its limit (b) Let a-V2, and define @n+1 = V2+@n for all n 1. Prove that lim an exists and equals 2 Hint: For both parts try to apply the Monotone Convergence Theorem
3. Consider the sequence (x,) with x, =3 defined recursively by the ruleX 4-x Explore the sequence with your calculator: a. 1 STO X STO 3-X ENTER, ENTER ENTER ENTER. 4-x Apparently the sequence diverges / converges to b. State the MONOTONE CONVERGENCE THEOREM: c. Use induction to show that (x) is decreasing for all n when x, 3 d. Use induction to show that (x.) is bounded below by 0 when x,- 3. e. Conclude from (b-d): d. To...
Please provide a detailed solution. Thanks in advance. (b) Let {Xn : n E N} b e a second order Markov chain, 1.e. , for all i,j, in-1,.. . ,i1 and for all n. Transform the state space so that the resulting process s first order Markovian.
(1) Give a careful, detailed proof of the following Proposition. The sequence {2jnEN s unbounded Your proof should use the Archimedean Property and Russell's Paradox (2) Working directly from the basic definition of convergence to a ->0o Vn y together limit, show that limn-+ n- r and lim, imply that limn→х (2xn-3y.) 2x-3y (3) Give a proof, by induction, of the following Proposition. For 0 〈 n E N. suppose that the functions fı, . . . , f,: R...
i need help with questions17, 18, 19 and 20 please !! Provide an appropriate response. 17) Suppose that an >O and b>0 for all na N(N an integer). If lim , what can you conclude 17) about the convergence of Yan? A) Yan converges it on converges B) Yar divergesit n diverges, and an converges it or converges Yan diverges if on diverges D) The convergence of an cannot be determined. Use the Ratio Test to determine if the series...
Please solve the exercise 3.20 . Thank you for your help ! ⠀ Review. Let M be a o-algebra on a set X and u be a measure on M. Furthermore, let PL(X, M) be the set of all nonnegative M-measurable functions. For f E PL(X, M), the lower unsigned Lebesgue integral is defined by f du sup dμ. O<<f geSL+(X,M) Here, SL+(X, M) stands the set of all step functions with nonnegative co- efficients. Especially, if f e Sl+(X,...
2. Let f(x 11 k 1 k-0 (a) Give the interval of convergence (b) Find a closed form for f(x) on the interval of convergence. Theorem 35: The series Eanbn converges if (a) The partial sums An of Ean are bounded, (b) bob1b2 (c) lim,00 bn = 0 0, 7
I need help with this Dynamics II electrical system analysis. Please provide detailed explanation and show work. Thank you. 3. Find the transfer function E, (s)/E, (s) of the circuit below using impedance methods Find expressions for the natural frequency a, and the damping ratio ζ . ei(t) For L-0.2H, 2 mF RI 10 ohms, R2 20 ohms, use MATLAB to calculatew, and ζ and then also plot the unit step response of the system. Apply the final value theorem...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1 Question 2 (10 marks) In this question you must state if you use any...