2 2n-1 n2+6n+8 Determine the exact value of the given infinite series: 10. D) 7 B)...
1 1. Find the exact sum of the following infinite series as indicated below: -1 1 1 1 1 + n(-4) 2(16) 3(64) 4(256) a. Let f(x) = 2n=1 (-1) x". I n a b. Find the power series for the derivative f'(x), and observe that it is a geometric series. Find its first term and common ratio. c. Use the formula 1-r to find an algebraic expression for f'(x). d. Integrate to find an algebraic expression for f(x). Make...
(1 point) In order to determine the convergence or divergence of the series (-6)" (n2 + 6n) 51+1 n=1 we calculate the limit I needed to run the Ratio Test. Which of the following values would we get? -6 A. L 30 6 B. L= olo olio C. L D. L= 0 E. L=0. F. the limit L does not exist. (1 point) Given that a function f(x) has a tangent line at x = 2 given by y =...
3. (20 points) Infinite Series (a) (10 points) Determine the convergence or divergence of the following series by applying one of the given test. Half credit will be given to those the correctly apply another test instead. (3)"e" (Limit Comparison Test or Root Test) (b) (10 points) Identify which two series are the same and then use the Ratio Test and/or Alternating Series Test to determine if the series is convergent or divergent A. (-1)" (n-1)2n-1 na2 B. (-1)"+1 n2...
Pt 1 pt 2 pt 3 pt 4 Please Answer every question and SHOW WORK! Determine whether the series n-1 Σ (2n)! 2". (2n! converge or diverge 1. both series converge 2. only series II converges 3. only series I converg es 4. both series diverge Determine whether the series 2! 1515.9 1-5.9-13 3! 4! 7m 1.5.9..(4n -3) is absolutely convergent, conditionally con- vergent, or divergent 1. conditionally convergent 2. absolutely convergent 3. divergent Determine which, if any, of the...
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...
Find the partial sums for each infinite series below: Infinite sometric Series 12 4 8 +1 +2 +4 + 8 + ... 16 s A series that approaches a certain sum is called a CONVERGENT SERIES A series that does not have a certain sum is called a DIVERGENT SERIES. then the series is then the series is nvergent Series Formula To find the sum of a convergent infinite geometric series, use the formula: Determine if the series is converent...
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
Use the information given about the angle 0,05 Os 2n, to find the exact value of sin (20). 31 cos = 21 29 <o<21 2 840 O A. 841 B. 41 841 840 841 D. 41 841
3) Determine whether the given series converges or diverges. i) (7 pts.] 4n2 + 3η +1 2n2 - η n=2 ii) (8 pts.] Σ 2n 11 COS NI iii) (10 pts.) ΠΕ1
(1 point) Select the FIRST correct reason on the list why the given series converges. D-1)", n 6 E 1 sin2 (3n) 2. n2 00 (п+ 1)(15)" 3. B 42n n-1 OC 6(6)" A 4. 2n 11 n 1 00 (-1)" In(e") п° cos(пт) C 5. n-1 1 D 6. п(m(n))? п-2 A. Geometric series B. Ratio test C. Integral test D. Comparison with a convergent p series. E. Alternating series test c2 (1 point) Select the FIRST correct reason...