Question 3 Let z + 3 (Z-0.7)(2+0.5) x (z) = - 121 >0.7 (1) Use partial_ fraction expansion to determine x[n]. given for (ii) If the region of convergence is insted by 121 <0.5, what would your answer part (i) be ?
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- (1 – )'. Graph y = f2(x) where f2(x) is the sum of the first two terms of the binomial expansion of: 2- -5 -4 -3 -2 -1 -1 -2 -3 -4- -5 ind Clear All Draw: 2. 7. 3.Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive. p = lim 287 TL-00 (n!)² 1(2n)! an+1 an is: A. convergent 2 (Enter 'inf for ∞o.) OB. divergent OC. The Ratio Test is inconclusive 7-1 (n!) ² (2n)!3.1f limnr+m Cn+1 2 Ihen EC" converges.
- Do the following scquences {a,} converge or diverge? Justify your answers. e" (a) an 3" (b) an = (-1)"/ñ 1 (c) an = (-1)" (d) an = (-1)2n+1 (-1)" + n (-1)" – n In (e*)") (e) an (f) an 3n (g) an = (-1)" cos (5(n + 1)) (;(2n + 1) (h) an = (-1)" sin(x-2) √x²+2x x-2) Converges? Dieverges? dx AND WHY?Find the interval of convergence of (x - 9)" In (9n) n=2
- Q.2)(A) Determine of each point convergens or diverges: (215) ² (5)(2+1) (-2)"(x-3)" Ο V(n + 1) 1=0 ΝΟ «Σ 170 sinhn (n²)coshn (5) ((Inn" – Inn)") 1703 21(a) Evaluate +7x²+10x dx by partial fraction method. .4 1 (b) Check the convergence of the improper integral 7 a dx. -x (x-2)2Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn = n cos Vn = (−1)” + For each of these six sequences, answer the following questions: (a) Give an example of a monotone subsequence. (b) Give its set of subsequential limits. (c) Give its lim sup and lim inf. (d) Is it bounded? 1/4 n