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Problem 4. Consider the series 1 +(x - 1/7) + „(x – 1/T)² + - (x – 1/x)³ + ... (a) Write the series in summation notation. (b) Determine the interval of convergence and the radius of convergence for the series.

Problem 4. Consider the series 1 +(x - 1/7) + „(x – 1/T)² + - (x – 1/x)³ + ... (a) Write the series in summation notation. (b) Determine the interval of convergence and the radius of convergence for the series.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Please solve only 4 broblme

1001 An Problem 3. Let {an}and {bn} each be a sequence of positive real numbers. You know that > bn converges and lim n→o bn 10 k=1 Your buddy Ron states that since the limit above is computed to be 1001, the series diverges by the ratio test. State whether Ron is correct or incorrect and explain why or why 10 not. Problem 4. Consider the series 1 + (x – 1/T) + (х —1/т)2 + "- (х — 1/т)3 — ... 3 (a) Write the series in summation notation. (b) Determine the interval of convergence and the radius of convergence for the series. Problem 5. Let f be a function that has derivatives of all orders at x = -3. Let Pn (x) denote the nth degree Taylor polynomial for f centered about x = -3. You are given f(-3) = 3, f'(-3) = –1, f"(-3) = 0 and f(4)(–3) = 3. Suppose P4(-5) = -1. Find P4(x).
Transcribed Image Text:1001 An Problem 3. Let {an}and {bn} each be a sequence of positive real numbers. You know that > bn converges and lim n→o bn 10 k=1 Your buddy Ron states that since the limit above is computed to be 1001, the series diverges by the ratio test. State whether Ron is correct or incorrect and explain why or why 10 not. Problem 4. Consider the series 1 + (x – 1/T) + (х —1/т)2 + "- (х — 1/т)3 — ... 3 (a) Write the series in summation notation. (b) Determine the interval of convergence and the radius of convergence for the series. Problem 5. Let f be a function that has derivatives of all orders at x = -3. Let Pn (x) denote the nth degree Taylor polynomial for f centered about x = -3. You are given f(-3) = 3, f'(-3) = –1, f"(-3) = 0 and f(4)(–3) = 3. Suppose P4(-5) = -1. Find P4(x).
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