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Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. Σ n = 1 хл nAgn Step 1 We are given the following power series and must determine the radius of convergence, R. Σ n = 1 хл nAgn Recall that a power series centered at a is of the form - (x − a)". The radius of convergence is the positive value R such that the power series converges if |× - a| < R and diverges if |x − a] > R. The given power series is n = 0 centered at (-49,49) Let an хл 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 n4gn To begin, find and simplify the limit. +7 +1 lim an + 1 = lim n∞o a, n→ ∞ (n + 1)4 9n+1 хл nAgn = = lim n→ ∞o (n + 1)4 lim 9 n→ ∞ ☑ n+1 X 9 4 an +1 an Tutorial Exercise Find the radius of convergence, R, of the series. 00 +7 +9 n = 2 9n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ an+1 an = lim n → ∞ xn+10 9(n + 1)! +7+9 9n! = xn+10 9 lim no9(n+1)! X7 +9

Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. Σ n = 1 хл nAgn Step 1 We are given the following power series and must determine the radius of convergence, R. Σ n = 1 хл nAgn Recall that a power series centered at a is of the form - (x − a)". The radius of convergence is the positive value R such that the power series converges if |× - a| < R and diverges if |x − a] > R. The given power series is n = 0 centered at (-49,49) Let an хл 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 n4gn To begin, find and simplify the limit. +7 +1 lim an + 1 = lim n∞o a, n→ ∞ (n + 1)4 9n+1 хл nAgn = = lim n→ ∞o (n + 1)4 lim 9 n→ ∞ ☑ n+1 X 9 4 an +1 an Tutorial Exercise Find the radius of convergence, R, of the series. 00 +7 +9 n = 2 9n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ an+1 an = lim n → ∞ xn+10 9(n + 1)! +7+9 9n! = xn+10 9 lim no9(n+1)! X7 +9

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
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Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. Σ n = 1 хл nAgn Step 1 We are given the following power series and must determine the radius of convergence, R. Σ n = 1 хл nAgn Recall that a power series centered at a is of the form - (x − a)". The radius of convergence is the positive value R such that the power series converges if |× - a| < R and diverges if |x − a] > R. The given power series is n = 0 centered at (-49,49) Let an хл 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 n4gn To begin, find and simplify the limit. +7 +1 lim an + 1 = lim n∞o a, n→ ∞ (n + 1)4 9n+1 хл nAgn = = lim n→ ∞o (n + 1)4 lim 9 n→ ∞ ☑ n+1 X 9 4 an +1 an
Transcribed Image Text:Find the radius of convergence, R, of the series. Then find the interval, I, of convergence of the series. Σ n = 1 хл nAgn Step 1 We are given the following power series and must determine the radius of convergence, R. Σ n = 1 хл nAgn Recall that a power series centered at a is of the form - (x − a)". The radius of convergence is the positive value R such that the power series converges if |× - a| < R and diverges if |x − a] > R. The given power series is n = 0 centered at (-49,49) Let an хл 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 n4gn To begin, find and simplify the limit. +7 +1 lim an + 1 = lim n∞o a, n→ ∞ (n + 1)4 9n+1 хл nAgn = = lim n→ ∞o (n + 1)4 lim 9 n→ ∞ ☑ n+1 X 9 4 an +1 an
Tutorial Exercise Find the radius of convergence, R, of the series. 00 +7 +9 n = 2 9n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ an+1 an = lim n → ∞ xn+10 9(n + 1)! +7+9 9n! = xn+10 9 lim no9(n+1)! X7 +9
Transcribed Image Text:Tutorial Exercise Find the radius of convergence, R, of the series. 00 +7 +9 n = 2 9n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ an+1 an = lim n → ∞ xn+10 9(n + 1)! +7+9 9n! = xn+10 9 lim no9(n+1)! X7 +9
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