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(1) Let ƒ(x) = x³₁· (i) Show that f(x): = −3.₁¹, and then use the geometric sum formula to expand f(x) into a series centered at a = 0. (ii) Use the Taylor formula for coefficients cn to obtain a series for f(x). (iii) Show that both sums obtained in (i) and (ii) are identical.

(1) Let ƒ(x) = x³₁· (i) Show that f(x): = −3.₁¹, and then use the geometric sum formula to expand f(x) into a series centered at a = 0. (ii) Use the Taylor formula for coefficients cn to obtain a series for f(x). (iii) Show that both sums obtained in (i) and (ii) are identical.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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(1) Let f(x) = ³1. 3 x-1 1 (i) Show that f(x) = −3.₁¹ 1-x into a series centered at a = = 0. and then use the geometric sum formula to expand f(x) (ii) Use the Taylor formula for coefficients cn to obtain a series for f(x). (iii) Show that both sums obtained in (i) and (ii) are identical.
Transcribed Image Text:(1) Let f(x) = ³1. 3 x-1 1 (i) Show that f(x) = −3.₁¹ 1-x into a series centered at a = = 0. and then use the geometric sum formula to expand f(x) (ii) Use the Taylor formula for coefficients cn to obtain a series for f(x). (iii) Show that both sums obtained in (i) and (ii) are identical.
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