102 Tist 2, Phne & of 6 Ma 11, 2019 (10) which of these is true about the series Σ n A. Converges to o B. Converges to C. Diverg D. Converges to F. Comverges to 4 E. Converges to 2 Question 3...
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
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...
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
6. If the sequence an converges, find the limit b. o C. 1 d. e. It diverges Find the sum of the convergent series: 7. Σ (hint a telescoping series) a 8. For a series Σ"。 find the sum if it converges (hint: a geometric series) 9. Determine the convergence (C) or divergence (D) of the sequences and series, respectively C.DCDC d. CCDC e. None of these
0-11 points RogaCalcET3 10.4.027. 8. Determine convergence or divergence by any method. Σ-7 -n3/3 7n n e n=1 The series converges The series diverges. 0-11 points RogaCalcET3 10.4.027. 8. Determine convergence or divergence by any method. Σ-7 -n3/3 7n n e n=1 The series converges The series diverges.
6. (25 points) Determine all positive values of p for which the series Lin=2 n(log2 n) 2. (15 points) Determine whether the sequence { v3.3.FI converges or not. If it n=1 converges, find the limit. If it diverges, specify whether it diverges to 00, -00, or neither. Is the sequence bounded? Explain. 4n+1 3. (15 points) Determine whether the series Emai gn=1 converges or not. If it converges, find the sum. 4. (10 points) Write 0.1257 as a fraction. 5.(20...
2. Test the Series for convergence or divergence. In(n) Σ(-) Σ- 4 n=3 η=1 n 3. Determine which option is absolutely converges and explain in details the reason. 1 (=Σ(-1)" 3 =Σ(-1)" C-Σ(-1)* tan(n) η Υ -Σ-1): E = None of these n!
Question 1 The series n²tn n=1 73/2+5n+1 converges. O True O False
Determine if diverges or converges. If it converges, find it limit a) an cos(2) b) an O n+1 c) an = (1 + n)" dan cos() e) an- f) an sen(5m) a) an cos(2) b) an O n+1 c) an = (1 + n)" dan cos() e) an- f) an sen(5m)
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...