Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. хл n4gn n = 1 Step 1 We are given the following power series and must determine the radius of convergence, R. 00 Σ n4gn хл n = 1 - - Recall that a power series centered at a is of the form Σ c(x − a)”. The radius of convergence is the positive value R such that the power series converges if |x − a| < R and diverges if |x − a] > R. The given power series is 00 n = 0 centered at хп Let an To begin, find and simplify the limit. be the terms of the given power series. By the Ratio Test, we know the convergence of the power series can be tested with the limit of nAgn an+1 an lim n→ ∞o an + 1 an lim n→ ∞o x7 +1 (n + 1)4 9n+1 xn nAgn = lim n→ ∞ (n + 1)4 = lim 9 noo = 1x ([ 9 n + 1 X × O 4

Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. хл n4gn n = 1 Step 1 We are given the following power series and must determine the radius of convergence, R. 00 Σ n4gn хл n = 1 - - Recall that a power series centered at a is of the form Σ c(x − a)”. The radius of convergence is the positive value R such that the power series converges if |x − a| < R and diverges if |x − a] > R. The given power series is 00 n = 0 centered at хп Let an To begin, find and simplify the limit. be the terms of the given power series. By the Ratio Test, we know the convergence of the power series can be tested with the limit of nAgn an+1 an lim n→ ∞o an + 1 an lim n→ ∞o x7 +1 (n + 1)4 9n+1 xn nAgn = lim n→ ∞ (n + 1)4 = lim 9 noo = 1x ([ 9 n + 1 X × O 4

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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