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a) We discussed in class that==1 x = 1 + x + x² + x³+.…... But if x=2 the following statement is clearly not true: Explain why the two statements don't contradict each other 1-2 ==₁2n = 1+2+4+8+....

a) We discussed in class that==1 x = 1 + x + x² + x³+.…... But if x=2 the following statement is clearly not true: Explain why the two statements don't contradict each other 1-2 ==₁2n = 1+2+4+8+....

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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1. Answer the wing questions. Clearly explain your reasoning. fo11 1 a) We discussed in class that==₁x¹ = 1+x+x² + x³+.... 1-x But if x=2 the following statement is clearly not true: 21-/₂2² = Σ=₁2¹=1+2+4+8+.... Explain why the two statements don't contradict each other b) What is the power series representation of the polynomial functionf(x) = 5x³ − 13x² + 10x - 5? What is its radius of convergence? Explain Test to determine the radius of convergence and the interval of convergence of the fol interval)
Transcribed Image Text:1. Answer the wing questions. Clearly explain your reasoning. fo11 1 a) We discussed in class that==₁x¹ = 1+x+x² + x³+.... 1-x But if x=2 the following statement is clearly not true: 21-/₂2² = Σ=₁2¹=1+2+4+8+.... Explain why the two statements don't contradict each other b) What is the power series representation of the polynomial functionf(x) = 5x³ − 13x² + 10x - 5? What is its radius of convergence? Explain Test to determine the radius of convergence and the interval of convergence of the fol interval)
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