Decide if the following series converge or not. Justify your answers using appropriate tests (12 marks):...
just C Decide if the following series converge or not. Justify your answers using appropriate tests (12 marks): (a) Lm=1 (In 2)" n3 1 (b) 2in=1 nyn+2 (c) 2 n=1 23n-1
(1) Decide if the following series converge or not. Justify your answers using appropriate tests (12 marks): m3 (a) In=1 (In 2) (b) = n(n+2 (c) L=123n1 1
1. Answer the following questions. Justify your answers. (a) (3 marks) For what values of x does the series 1 + 22x 2 + 24x 4 + 26x 6 · · · + 22nx 2n + · · · converge? (b) (9 marks) Is the following series absolutely convergent, conditionally convergent or divergent? i. X∞ n=1 2 √ n − 2 √ n + 1 ii. X∞ n=1 arctan(n) n2 + 1 iii. X∞ k=1 (−1)k k 1. Answer the...
1. For each part of this question carefully justify your conclusions by referring to the appropriate tests or standard limits. (a) Determine whether the following series converges or diverges: n sin2 n 73-7 rl n-3 b) For which integer values of p does the following series converge? 00p)! n+p)m 1. For each part of this question carefully justify your conclusions by referring to the appropriate tests or standard limits. (a) Determine whether the following series converges or diverges: n sin2...
In this question carefully justify your conclusions by refering to the appropriate tests. (a) Determine whether the following series converges or diverges: (to infinity) (n*(sin(n))^2)/((n^3)-7) (b) For which integer values of p does the following series converge? (to infinity)((2^(pn))(n+p)!)/(n+p)^n please write your answers on a piece of paper and take a photo for clarity. n=3 We were unable to transcribe this image
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
1. For each part of this question carefully justify your conclusions by referring to the appropriate tests or standard limits. (a) Determine whether the following series converges or diverges: n sin2 n (b) For which integer values of p does the following series converge? oo 2pm (n +p)! n lpl
(a) (6 marks) Does the series (–19* sin( , ) converge or divergor Justi (a) (6 marks) Does the series converge or diverge? Justify your answer and state any test(s) you used. (-1)" cos(4n) (b) (2 marks) Consider the series . Explain why the Alternating Series Test can NOT be consider the senes 2 2n3 . used to determine whether the series converges or diverges.
Please try to do all parts. Thanks! ple 2. Find 3. Determine which of the following series converge. Justify your conclusions with the appro -1)" In n (c) Σ dots not 4. Suppose we know that 0 S on S 1/n S an and that 0sn S1/n2 sd for all n. (a) Which of the series Σα", Σ h,De-, and Σ d" definitely converge? Justify your answer. (b) Which of the series Σα", Σ " Σ c", and Σ d"...
1. Answer the following questions. Justify your answers. a. (8pts) Find the Taylor series for f(x) = (5x centered at a = 1 using the definition of the Taylor series. Also find the radius of convergence of the series. b. (8pts) Find a power series representation for the function f(x) = 1 5+X C. (4pts) Suppose that the function F is an antiderivative of a function f. How can you obtain the Maclaurin series of F from the Maclaurin series...