2. Prove by Mathematical Induction that: 2.1 4 +95m, m≥ 3 2.2 1x² < (n²)(n+1)², n ≥ 2 2.3 2-7> 10n, m = n, n ≥ 7
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A: Explanation given in step 2
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- 3. Let p(n) = Σª a¡n², where a¿ > 0, be a degree-d polynomial in n, and let k be a constant. Prove the following properties. if k ≥ d, then p(n) = 0(nk); if k ≤d, then p(n) = N(nk); if k = d, then p(n) = 0(nk); if k > d, then p(n) = o(n²); if k < d, then p(n) = w(nk); a. b. C. d. e.For x = [7 3 9 10 15] and y= [18 2 9 12 4], what is obtained for z when using z = find(xProblem 1. True or False? Justify your answer briefly. a. n 3 + 2n 2 ∈ ω(0.1n 3.1 + n) b. n log5 n ∈ Θ(n 5 4 ) c. 2 n log n ∈ Θ(4n ) d. For any constant a > 1: a n+1 ∈ o(n!). e. √ log n ∈ o(log(√ n))prove that for every integer n >= 1 n sum i=1 (2i-1) = n^2Formally prove or disprove the following claims a) logs (n³) is O(n), for n ≥ 1 b) 3" is (n) for any real constant k > 1Computer Science Can someone show me these two? 3. Compute the sum E {1 / (i²-1) : 2Question 2: Find y[n]=x[n]*h[n] x[0] = 2, x[1] = 3, x[2] = 5, x[n] = 0 for all other integers (n). h[0] = 2 , h[1] = 2, h[2] = -1, h[3] = 4, h[n] = 0 for all other integers (n). %3D %3D %3DProvide me complete and correct solution of question thanks 3If the region of convergence of x1 [n] + x2 [n] is 1/3 < |z| <2/3 , then the region of-3 convergences of x1[n] – x2[n] includes 2 < |z<3 3 0 خيار 1 2 3 <3 <3 3 O خیار 4 O خيار 3Recommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
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