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According to the Limit Comparison Test, when a, > 0 and b, > 0, and a lim = L, n- 00 in where L is finite and positive, then the two series Fa and b either both converge or both diverge. n We will compare the given series to which converges as it is a geometric series with |r| < 1. n = 1 and b, = G)". 9" + 1 (금 Let a in Substitute the values of a and b, n' apply the limit n → ∞, and simplify it. in 2 9" + 1 lim lim 1 n- 00 n→ 00 2· 9" lim n- 00 + 1 %3D

According to the Limit Comparison Test, when a, > 0 and b, > 0, and a lim = L, n- 00 in where L is finite and positive, then the two series Fa and b either both converge or both diverge. n We will compare the given series to which converges as it is a geometric series with |r| < 1. n = 1 and b, = G)". 9" + 1 (금 Let a in Substitute the values of a and b, n' apply the limit n → ∞, and simplify it. in 2 9" + 1 lim lim 1 n- 00 n→ 00 2· 9" lim n- 00 + 1 %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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According to the Limit Comparison Test, when a, > 0 and b, > 0, and n n a lim L, n→ 00 where L is finite and positive, then the two series a and b, either both converge or both diverge. in We will compare the given series to 1 which converges as it is a geometric series with Ir| < 1. 9n' n = 1 Let a n and bn . Substitute the values of a, and b,, apply the limit n → ∞, and simplify it. n' 9" + 1 a 9' + 1 lim lim 1 n→ 00 n- 00 2· 9" lim n> 00 + 1
Transcribed Image Text:According to the Limit Comparison Test, when a, > 0 and b, > 0, and n n a lim L, n→ 00 where L is finite and positive, then the two series a and b, either both converge or both diverge. in We will compare the given series to 1 which converges as it is a geometric series with Ir| < 1. 9n' n = 1 Let a n and bn . Substitute the values of a, and b,, apply the limit n → ∞, and simplify it. n' 9" + 1 a 9' + 1 lim lim 1 n→ 00 n- 00 2· 9" lim n> 00 + 1
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