22. Which of the following statements about convergence of the series 00 1 (Α) Σ n=1 In (n+1) converges by comparison with Σ n n=] 00 (Β) Σ 1 00 n=1 In (n + 1) converges by comparison with n=1n 8 1 (Ο) Σ diverges by comparison with n=1 In (n + 1) -= n=1 00 1 (D) Σ diverges by comparison with n=1 In (n + 1) n=1n is true? n=1 In (n + 1)
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- Consider the power series (x-2) (x - 2)² 2 + (x - 2)³ 3 3. What is the radius of convergence? (x - 2)¹ 4 1. Write this series as a single sum of the form Σck. (x-2)^. k=1 +... 2. Use the Ratio Test to determine the interval of convergence of this power series.Q5/ For the following series :- 1 (x-2), (x - 2)2 (x- 2)" f(x). + (-1)". - 4 8 2n+1 Find :- a- Values of (x) that make series converged b- The sum of series Ans./ a) 0Suppose that Cnxn converges when x = -4 and diverges when x = 6. What can be said about the convergence or divergence of the following series? n = 0 (a) When compared to the original series, we see that x = here. Since the original series: ---Select--- ifor that particular value of x, we know that this series ---Select--- (b) When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series ---Select--- ---Select-- (c) Cn(-2)" n= 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series ---Select--- ---Select--- (d) (-1)"C,9 When compared to the original series, we see that x = here. Since the original series ---Select- for that particular value of x, we know that this series ---Select---For the included problem, I keep getting that the series converges, but the correct answer is that it diverges. I used both the limit comparison test and the root test and got that it converges both times with these tests. How does the series diverge and what test should I use? Σ(k=1 to infinity) of (2k+k)/(4k^4-8k)Determine the rate of convergence of the sequence an sin( 2n+3) as n+ 00. n-5 %3D A. O(1/n) B. O(n) C. O(1/n^3) O D. 0(1/n^2) Reset SelectionThe series True O False (-1)^ n Σn=1 is conditionally convergent.Show that 2n=0 3(2)n+2 is convergence and Σ= 3(2)n+2 20. %3D 5"Suppose that the series ax has radius of convergence 5 and (a) (b) 2 (an+b)xn n=1 n=1 (c) bn(x - 2)4n n=1 n=1 R = an(x-7) R = R = n=1 box has radius of convergence 9. Find the radius of convergence of the following series.Let 2 C,(x-9)" be a power series with the radius convergence R=0. Then n =0 Select one: a. The series C(x-9)" is convergent at x = - 9 b. None of them The series 2 Cn(x-9)" is convergent at x = 0 n = 0 d. The series 2 c,(x - 9)" is divergent at x = 9 n =0 e. The series C(x-9)" is convergent at X =9 n=0SEE MORE QUESTIONS