Assuming |z| < 1, show that 1 1+2² -Σ = Σ(-1)" 27. =0 Hence find a power series formula of aretan(r), valid for a € (-1, 1).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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plz provide answer for ques 5 asap

(a) Assuming || < 1, show that
1
1+z²
∞
-£- Σ(1)" 2".
=
n=0
(b) Hence find a power series formula of arctan(x), valid for r € (-1, 1).
Transcribed Image Text:(a) Assuming || < 1, show that 1 1+z² ∞ -£- Σ(1)" 2". = n=0 (b) Hence find a power series formula of arctan(x), valid for r € (-1, 1).
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