Given x(z) = (zˆ2+1)/(z-1/2) Find y(n) = x(2n).(1/2)ˆn and w(n) = cos(pi.n/2).x(n)
2. Simplify: (n + 2)! (1) n! (2n-1)! (2) (2n + 1)! (2n + 2)! (3) (2n)!
Prove: without using l'hopital's rule. infinity 2n-1 ln(2) (2n-1) n infinity 2n-1 ln(2) (2n-1) n
Question 3 [10 marks Let W Then the p.d.f. 1 fw (w) 2"/21 (n/2) exp(-w/2) w3-1, w>0. and the c.d.f. is denoted as Fw (w) (a) Show that 0, n > 0, and (i) The function fw(w) is a p.d.f. (i.e., that fw(w) 2 0 for w Jo fw(w)dw 1). (ii) The mode of W is n - 2 for n > 2. (b) As n oo, W becomes normally distributed with mean n and variance 2n. This has led...
8. Use induction (on n) to show that: (a) (2n)! > 2" (n!)?, for n > 0. (w) (%) = (2+1), for os ms m. (0) Ž -»* (*) = (–1"("m"), for os m<n.
Given the following quantities: Q, W, U, Ek write down which one of the following statements is true: (A) Q always equals W if U = 0 (B) Ek is always zero or positive (C) all of the quantities can have a negative value (D) Q always equals U (E) only two of the quantities can have a negative value
Help 2. = n(n+1)(2n+1) Cr=-=n(n+1) r(21-1) Given - and PT find in terms of e are integers (bn' + en + dn+e) Write your answer in the form a where a, b, possibly zero. Then b= d = and e = Part 2: 2
--Red In( - ) () -2 21 (+1) 2+1(n + m)} ml(m + 2n + 1) (1 - 1) de 22+1(n!) (2n +1) 8. By evaluating ac 2h +G ah where G(h) is the generating function for Legendre polynomials, show that 1 - 2 Σ (2n +1) Po (1 - 2ch + ha) Hence, or otherwise, prove that Pn(x) dx 2h 9. Given that {(2, 2) = ( 12h the hm-dh m>1. prove that 2am+ | 112,0)P.a)dt (m + n)...
Find the first four terms of the sequence given by the following. 21,=(-1)". 2n', n=1, 2, 3,... 0.000 OO Х 5
J W wiu ZUUU U m Bom l The Doctor ordered 20meq Kel to be given over 8hrs period by TV drip in 1000ml of D5W to a "client after surgery. The IV equipment is calibrated at 20 drops/ml. To deliver the correct dose the solution must be set to flow at the rate of? ----- M The nurse is to infuse 400ml of lactated Rinner at 50ml ner hour The infusion stated at 0800