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1.1.12 Recall the geometric series asloilloco (opne 1 1+x+x+x*+……= 1-X whenever x| < 1. (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,x²,x2,...} of func- tions from (-1,1) to R is linearly independent.

1.1.12 Recall the geometric series asloilloco (opne 1 1+x+x+x*+……= 1-X whenever x| < 1. (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,x²,x2,...} of func- tions from (-1,1) to R is linearly independent.

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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Plz solve only b part within 30-40 mins I'll give you multiple upvote
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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