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4. Recall the geometric series formula for all r <1, i.e. -1

4. Recall the geometric series formula for all r <1, i.e. -1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Recall the geometric series formula Σ* = k- x (a) Suppose that 2 € (-1,1) show that (-1)** for all r <1, i.e. -1<r<1. Use this formula for the following: 1 1+z (b) Use the result from part (a) to find a series representation for the function f(z) 2²2 2+1 (e) (Optional challenge question) The derivative of f(z) in part (b) is the function f'(r) = guess for a series representation of f'(2), 2€ (-1,1)? 2² (1+1), 200 27:² 21² + 1x (x + 1)² ,r€ (-1,1). What is your best
Transcribed Image Text:4. Recall the geometric series formula Σ* = k- x (a) Suppose that 2 € (-1,1) show that (-1)** for all r <1, i.e. -1<r<1. Use this formula for the following: 1 1+z (b) Use the result from part (a) to find a series representation for the function f(z) 2²2 2+1 (e) (Optional challenge question) The derivative of f(z) in part (b) is the function f'(r) = guess for a series representation of f'(2), 2€ (-1,1)? 2² (1+1), 200 27:² 21² + 1x (x + 1)² ,r€ (-1,1). What is your best
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