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1.1.12 Recall the geometric seriesnsloillooo.(opino 14x+x+x+..= 1 whenever x| <1. 1-X (a) Why does the above expression not imply that 1/(1-x) is a linear combination of 1, x, x2, ...? (b) Show that the set {1/(1-x), 1,x,x2,x,..} of func- tions from (-1,1) to R is linearly independent.

1.1.12 Recall the geometric seriesnsloillooo.(opino 14x+x+x+..= 1 whenever x| <1. 1-X (a) Why does the above expression not imply that 1/(1-x) is a linear combination of 1, x, x2, ...? (b) Show that the set {1/(1-x), 1,x,x2,x,..} of func- tions from (-1,1) to R is linearly independent.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1.1.12 Recall the geometric series oillu (oopin 1 whenever x| < 1. 1+x+x+x+•..= Sow sd 1-x (a) Why does the above expression not imply that 1/(1-x) is a linear combination of 1, x, x,...? (b) Show that the set {1/(1-x), 1,x,x,,...} of func- tions from (-1,1) to R is linearly independent.
Transcribed Image Text:1.1.12 Recall the geometric series oillu (oopin 1 whenever x| < 1. 1+x+x+x+•..= Sow sd 1-x (a) Why does the above expression not imply that 1/(1-x) is a linear combination of 1, x, x,...? (b) Show that the set {1/(1-x), 1,x,x,,...} of func- tions from (-1,1) to R is linearly independent.
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