Consider the function g(x) = (1-x)². Show that 1 (1 - x)² = 1+2x+3x²+ + (n +1)x+ n+2 (n+1)x (1 - x)² - -xn+1

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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Consider the function g(x)
1. Show that
1
(1 − x)²
1
= (1-x)².
1 + 2x + 3x² + +(n+1)x² +
n+ 2 −(n+1)x n+1
(1-x)²
2. Find the n-th Maclaurin polynomial for g by using the alternative definition of Taylor poly-
nomial (with the big O).
Transcribed Image Text:Consider the function g(x) 1. Show that 1 (1 − x)² 1 = (1-x)². 1 + 2x + 3x² + +(n+1)x² + n+ 2 −(n+1)x n+1 (1-x)² 2. Find the n-th Maclaurin polynomial for g by using the alternative definition of Taylor poly- nomial (with the big O).
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