1. Answer the following questions. (A) [50%] (Telescope series) Consider the series Σ n=4 3 n(n - 1) (i) Find the sequence of partial sums {8}4. Hint: You may write the series terms as an addition of partial fractions. (ii) Use {8}4 to determine if the series diverges or converges. If the series converges, find its sum. (B) [50%] Consider the series ✗ 3nxn n=0 (i) Find the values of x for which the series Σ 3" x " converges. n=0 (ii) Find the sum of the series. Remark: The series sum should be a function of x. (iii) Determine if the sum obtained in Part (ii) can be used to calculate ✗3" (x*)" when ∞ x*= -0.2,0.5. If so, to 3 decimals find Σ 3" (x*)". n=0 n=0

1. Answer the following questions. (A) [50%] (Telescope series) Consider the series Σ n=4 3 n(n - 1) (i) Find the sequence of partial sums {8}4. Hint: You may write the series terms as an addition of partial fractions. (ii) Use {8}4 to determine if the series diverges or converges. If the series converges, find its sum. (B) [50%] Consider the series ✗ 3nxn n=0 (i) Find the values of x for which the series Σ 3" x " converges. n=0 (ii) Find the sum of the series. Remark: The series sum should be a function of x. (iii) Determine if the sum obtained in Part (ii) can be used to calculate ✗3" (x)" when ∞ x= -0.2,0.5. If so, to 3 decimals find Σ 3" (x*)". n=0 n=0

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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