1. (6 points- 3 points each) Determine the radius of convergence and the interval of convergence for each series listed below: (a) ∞ (−1)n(2x − 4)2n n=1 n3n (b) ∞ (x−7)n2n 1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed below: (a) Σ (-1)-(2x-4)2n 2 conve n3n n-1 3n2 1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed...
For problems 5 and 6 find the radius of convergence and the interval of convergence 5. 5 (x-3)n V n=0 n3n TS r3n+1 (2n - 1)(2n +1)
Find the interval and radius of convergence of the power series (x + 1)k 3k 22 k-1
La Use the rako test to show convergence / divergence of the senes oo (an-1) In: 4 h - 6) determine whether as (-1)" is convergent or divergent. If convergent insi ova is it absolute Or Conditional? 7) Find the radius of convergence for the following power senes: a) 8 / 2x)" bg (x+2)n Inol 7 8) and the interval of contergence for the following power series i no Lan)
Question 1 (10 points) Find the radius of convergence and the interval of convergence of the following power series. Make sure to clearly indicate and justify whether or not the end points of the interval are included in the interval of convergence. (3.7 - 6)" 2+1 The radius of convergence is: The interval of convergence is: Page 2
Find the radius of convergence and the interval of convergence of the following power series. Make sure to clearly indicate and justify whether or not the end points of the interval are included in the interval of convergence. Σ (3.0 - 6)" 2n n +1 n=1
What is the interval of convergence, radius of convergence and are the endpoints included or not? Σ (3.0 – 6)" 2η γη +1 n=1
Power Series - Interval of Convergence Exercise Step 1 Find the radius of convergence R, and interval of convergence I of the series. First, set up the limit: 100 lim 1+1 10"+1(n+1) ( +1) n 18 Step 2 Evaluate the limit. lim 10 (n + 1) 10"n Submit Skip.(you cannot come back)
Problem 7. (10 points) Find the center, radius of convergence and interval of convergence for the power series IM8 (-1)'(x - 1)" m2 +1 Center: x = Radius of Convergence: Interval of Convergence (use interval notation): Note: You can earn partial credit on this problem. Problem 8. (10 points) Find the Taylor polynomial of degree 2 for $(x) = + x centered at a -6. 73(x) =
Find R, the radius of convergence, and the open interval of convergence for: Σ The series has the open interval of convergence of (-2,2). Determine if the series converges or diverges at each endpoint to find the full n=1 interval of convergence. n. .2" At x = -2 the series converges At x = 2 the series diverges The interval of convergence is M Find R, the radius of convergence, and the open interval of convergence for: (2x - 1)2n+1...