The number of non-empty subsets of Bis 2 |{S:SC A, |S| = 2 and Sn B=0}|= 2 max {|S| : S C AUB, |SN A| is even and |Sn B| is even} = 4

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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A: given that (1) (a)                                    S=n(-1)n:n∈N=2k(-1)2k:n=2k,…

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Q: 4. Prove that for n > 0: E, 2* = 2"+1 – 1. sk3D0

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Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

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Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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Q: The number of non-empty subsets of B is |{S:SC A, S = 3 and Sn B = 0}| = max {|S|: SC AUB, SNA| is…

A: Given that A and B are finite sets satisfying A=6, B=7, A∩B=2. Since, B=7. So, total number of…

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Q: 4) Which of the following foumulas does not Kold for all x, we CZ O la wl= |2). Iw). (6) X W = ņ. W.…

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Q: Then, we assume that Wn+1 - H Wn - l kn+1 kin 1 2 E Wn-p Wn-p p=0 p=1 (6) n+1 - € Zn - € Vn+1 = 1 Vn…

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Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

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Q: Prove that for Vr > 0, s > 0, √√r + √√5 ± √√r + s r, s

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: The largest interval for which the IVP: (In(e* – e)) y' + y = 1, y(5) = 0 %3D X-6 has a unique…

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Q: Let Xionne Xn be aris H c'cid) From PlO), or QcOi Findthe MP test g sige a to test Ho:G-Be N5 H,:…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

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Q: Suppose that, based on your roommate's expert knowledge, you set the ROPE for O at (-5, 5). Suppose…

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Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

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A: Given:  ut = uxx, 0 < x < 1, t > 0,  u(0, t) = 1, u(1, t) = t, t > 0,  u(x, 0) = 1 +…

Q: * السؤال The largest interval for which the IVP: (In(e* – e²)) y' + y = 1, y(5) = 0 has a unique…

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Q: Prove that the set S = {n² : n E N} is denumerable.

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Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

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Q: 1). If r is not equal to one, show that a + ar + ar^2+ ....+ ar^n= a( r^n+1 -1)/( r-1).2).…

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Q: (3) Let A be m x n (not need to be square). What is the sum of the diagonal elements of ATA in terms…

A: (3) Given that Abe m×n matrix (not need to be square matrix). We have determine the sum of the…

Q: Theorem 5 there is auniqe Reul for X=2 Sit X ER

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Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

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Q: Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use…

A: Cauchy-Swartz Lemma : For any real numbers  and  the following inequality holds  ,

Q: Prove: If s S6sn for all n EN and if both sn Land un+ L, where LE R, then t - L asn- 0 as well. That…

A: We are given that sn≤tn≤un  for all n ∈ℕ and both sn and tn converges to L∈ℝ.We need to show that tn…

Q: Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn…

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Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

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Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n

Q: consider the propaitiau for S=E an, where Sy = Ean is its K-th partalsu Sumy I-If Rim Sx-0, so the…

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