Answered: ΣΗ on the interval (-3, 3) 37. n=0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.5: Trigonometric Form For Complex Numbers

Problem 5E

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Question

Expert Solution

Given

$T h e g i v e n p o w e r s e r i e s i s \sum_{n = 0}^{\infty} \frac{x^{n}}{3^{n + 1}}$

Theorem

$L e n a_{n} b e a s e q u e n c e o f r e a l n u m b e r s, t h e s e r i e s \sum_{n = 0}^{\infty} a_{n} x^{n} i s c a l l e d t h e p o w e r s e r i e s . h e r e, α = \lim_{n \to \infty} {|a_{n}|}^{\frac{1}{n}} a n d R = \frac{1}{α} . T h e n t h e p o w e r s e r i e s c o n v e r g e s i n t h e i n t e r v a l (- R, R)$