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Apply the alternating series test to discuss convergence or divergence of the given series. Σ(−1)n+1 ¹ nº n=1

Apply the alternating series test to discuss convergence or divergence of the given series. Σ(−1)n+1 ¹ nº n=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Apply the alternating series test to discuss convergence or divergence of the given series. Ο α Σ(-1)"+1 n=1 O O O h=. Since M8 Σ (-1) n=1| Since Since 1 n=1 n4 α Σ (-1) n =] (-1)' ) "+1 Since n=1 h Σ (-1) n=1 n+1 το 1 n=1 n' Σ (-1) n=1 1 n 00 1 n+1 n=1 n' converges, then the original series is absolutely convergent. n+1 η 1 · diverges, then the original series is divergent. 1 n² +1 n 1 Σ which is a convergent p-series. n=1 n' 00 Σ n=1 ht n- 1 2 ∞0 1 Σ n=1 n2 converges, then the original series is conditionally convergent. Σ n=1 which is a divergent harmonic series. 1 which is a convergent geometric series. 1 -Σ. η n=1 h diverges, then the original series is divergent. which is a divergent p-series. which is a convergent p- series. 00 1 Since Σ converges, then the original series is conditionally convergent. n=1 n°
Transcribed Image Text:Apply the alternating series test to discuss convergence or divergence of the given series. Ο α Σ(-1)"+1 n=1 O O O h=. Since M8 Σ (-1) n=1| Since Since 1 n=1 n4 α Σ (-1) n =] (-1)' ) "+1 Since n=1 h Σ (-1) n=1 n+1 το 1 n=1 n' Σ (-1) n=1 1 n 00 1 n+1 n=1 n' converges, then the original series is absolutely convergent. n+1 η 1 · diverges, then the original series is divergent. 1 n² +1 n 1 Σ which is a convergent p-series. n=1 n' 00 Σ n=1 ht n- 1 2 ∞0 1 Σ n=1 n2 converges, then the original series is conditionally convergent. Σ n=1 which is a divergent harmonic series. 1 which is a convergent geometric series. 1 -Σ. η n=1 h diverges, then the original series is divergent. which is a divergent p-series. which is a convergent p- series. 00 1 Since Σ converges, then the original series is conditionally convergent. n=1 n°
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