Power series can be used to evaluate certain infinite series. An example is ∞Σ n=1 n/5^(n-1) a) Find a power series representation of 1/(1-x)^2 by differntiating the power series representation of 1/(1-x). What is the interval of convergence for the power series of 1/(1-x)^2? b) Use the your awnser in part (a) to find the sum of ∞Σ n=1 n/5^(n-1). Also, to clear up any confusion, infinity is supposed to be on top and n=1 is on the bottom.

Power series can be used to evaluate certain infinite series. An example is ∞Σ n=1 n/5^(n-1) a) Find a power series representation of 1/(1-x)^2 by differntiating the power series representation of 1/(1-x). What is the interval of convergence for the power series of 1/(1-x)^2? b) Use the your awnser in part (a) to find the sum of ∞Σ n=1 n/5^(n-1). Also, to clear up any confusion, infinity is supposed to be on top and n=1 is on the bottom.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 22RE

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