Question 4. (1+(1+2+1) marks] Using the formulas for known series, find the sum of the following...
just question 3 2. (9 marks) This question is about infinite series. (a) Explain what it means for an infinite series Σ a, to converge to the sum L E R. (b) For the series 2ー, write down a formula for the kth partial sun 5.- (c) Using your answers to parts (a) and (b), show that Σ n'tn-1. Hint for Part (b: what is T12 -1 91 nn+1 We were unable to transcribe this image 2. (9 marks) This...
5. (12 marks) Determine whether the given series is convergent, If so, find its sum. a. Σ=4 η2-1 -η 6. Σ. 52 () C. Σ=5 4η νη+100
Find the sum of the finite geometric series using the formula for Sn Σ 2(105/-1 i- 1 The sum of the finite geometric series is Sn (Round to four decimal places.)
1 1 1 [3 marks] 32.. 1 (a) Find the sum to infinity of the series 2-3+ [3 marks] (b) Show that x+ 2x + 3x + ... + x = nx(n+1) (c) Show that Esin'(x) = sing if \sin xkl. [3 marks]
(a) Starting with the geometric series X?, find the sum of the series η ΕΟ Σ ηχο – 1, 1x] <1. ΠΕ 1 (b) Find the sum of each of the following series. DO Σηχή, 1x <1 η = 1 η (i) Σ. (c) Find the sum of each of the following series. D) Σπίη – 1)x, Ix <1 ΠΕ 2 (i) Σ - η 57 ΠΕ 2 0 i) 22 = 1
Find a power series representation centered at O for the following function using known power series. Give the interval of convergence for the resulting series. 2 f(x) 2+x Which of the following is the power series representation for f(x)? ΟΑ. Σ(3) OB. 2 ko OC. (-2011 OD. (-x?)" The interval of convergence is (Simplify your answer. Type your answer in interval notation)
please answer question 34 only (-1) 33. Find the sum of the series correct to four decimal places. 34. (a) Show that the series & 2m) is convergent. (b) Deduce that lim0 (2n)! 35. Prove that if the series Σ-a, is absolutely convergent, then the series n+ 1 (-1) 33. Find the sum of the series correct to four decimal places. 34. (a) Show that the series & 2m) is convergent. (b) Deduce that lim0 (2n)! 35. Prove that if...
Find the sum of each geometric series: ΣXe) n +3 Σ-5 b) 50 n-0 n-1 Find the sum of each geometric series: ΣXe) n +3 Σ-5 b) 50 n-0 n-1
Σ(4+2-ris convergent and find Solve the largest region in which the series (a) its sum. Compute or evaluatethe contour integraltoshowoL,tieng (b) (n+1)! Σ(4+2-ris convergent and find Solve the largest region in which the series (a) its sum. Compute or evaluatethe contour integraltoshowoL,tieng (b) (n+1)!
Which of the following series diverges? n +2 2n -1 n1 n+3 O A. 2 B. O C. 1,3 O D. 1, 2 OE. 2, 3 F. None O G. O H. 1,2,3 Find the sum of the series A. B. OC. 1/10 D. 1/2 3/2 3/4 OE. 1 F. 5/12 OG. 1/4 H. Divergent Which of the following series converges? oo 2n 1.Σ n 1 23n nE1 (n+ 1)3 n+ 1 3. O A. None O B. 2 O...