For what values of x does the following infinite geometric series converge (i.e., find the interval of convergence)? Provide thorough reasoning. a) 1 + (x + 1) + (x + 1)2 + (x + 1)3 . . . b) 1 + (x - 2) + (x - 2)2 + (x - 2)3 . . .

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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For what values of x does the following infinite geometric series converge (i.e., find the interval of convergence)? Provide thorough reasoning.

a) 1 + (x + 1) + (x + 1)2 + (x + 1)3 . . .

b) 1 + (- 2) + (- 2)2 + (- 2)3 . . .

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