(a) What does it mean for a series to be absolutely convergent? Σ a, is absolutely convergent if ✗ a, diverges and _ la_l diverges. n n Σ an is absolutely convergent if _ _ __ converges and Σ lan) converges. n an Σ an is absolutely convergent if ☐ a, diverges but ☐ la,l converges. n is absolutely convergent if _ a, converges but Σ lal diverges. (b) What does it mean for a series to be conditionally convergent? n n is absolutely convergent if Σ a, diverges and Σ lal diverges. n , is absolutely convergent if Σ a, diverges but Σ lal converges. Σ a, is conditionally convergent if n Σ an is conditionally convergent if 'n converges but Σ lal diverges. (a, converges and Σ lal converges. n 00 bconverges, then what can you say about the series Σ(-1)? (c) If the series of positive terms 00 n = 1 n ∞ Σ (-1)^b, is absolutely convergent. n = 1 n = 1 00 (−1)b is conditionally convergent. n n = 1 Σ (-1)^/, converges, but more information is needed to determine if it is absolutely or conditionally convergent. n = 1 ∞ ○ More information is needed to determine if Σ (-1)^/b_ converges or diverges. n = 1 n

(a) What does it mean for a series to be absolutely convergent? Σ a, is absolutely convergent if ✗ a, diverges and _ la_l diverges. n n Σ an is absolutely convergent if _ _ __ converges and Σ lan) converges. n an Σ an is absolutely convergent if ☐ a, diverges but ☐ la,l converges. n is absolutely convergent if _ a, converges but Σ lal diverges. (b) What does it mean for a series to be conditionally convergent? n n is absolutely convergent if Σ a, diverges and Σ lal diverges. n , is absolutely convergent if Σ a, diverges but Σ lal converges. Σ a, is conditionally convergent if n Σ an is conditionally convergent if 'n converges but Σ lal diverges. (a, converges and Σ lal converges. n 00 bconverges, then what can you say about the series Σ(-1)? (c) If the series of positive terms 00 n = 1 n ∞ Σ (-1)^b, is absolutely convergent. n = 1 n = 1 00 (−1)b is conditionally convergent. n n = 1 Σ (-1)^/, converges, but more information is needed to determine if it is absolutely or conditionally convergent. n = 1 ∞ ○ More information is needed to determine if Σ (-1)^/b_ converges or diverges. n = 1 n

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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