q11-sol-1042-sp08

q11-sol-1042-sp08 - Calculus II—1042 Solution of Quiz #...

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Unformatted text preview: Calculus II—1042 Solution of Quiz # 11 Fri., 04/11/08 1. Determine if the Geometric series convergent or divergent. If convergent, find its sum. (a) ∞ X n =1 (- 1) n (3) n- 1 4 n +1 . Solution: It is a Geometeric Series with starting point n = 1. First write the series in a correct form ∞ X n =1 ar n- 1 ∞ X n =1 (- 1) n (3) n- 1 4 n +1 = ∞ X n =1 (- 1)(- 1) n- 1 (3) n- 1 4 2 · 4 n- 1 = ∞ X n =1- 1 16 ¶- 3 4 ¶ n- 1 Now a =- 1 16 and r =- 3 4 so the Series is covergent as | r | = 3 4 < 1 and Sum =- 1 16 1-- 3 4 =- 1 28 (b) ∞ X n =0 π n e n +1 . Solution: It is a Geometeric Series with starting point n = 0. First write the series in a correct form ∞ X n =0 ar n ∞ X n =0 π n e n +1 = ∞ X n =0 π n e · e n = ∞ X n =0 1 e ¶ ‡ π e · n a = 1 e and r = π e so the Series is divergent as | r | = π e > 1 2. Find the values of x for which the given Geometric series ∞ X n =0 4 x- 3 2 ¶ n converges. Find the sum of the series for those values of x ....
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This homework help was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

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q11-sol-1042-sp08 - Calculus II—1042 Solution of Quiz #...

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