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Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (1 n+1 (2) Use part (1) to compute the n-th partial sum sn. (3) Deduce that 1 an converges and state its value. -) for each n ≥ 2.

Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (1 n+1 (2) Use part (1) to compute the n-th partial sum sn. (3) Deduce that 1 an converges and state its value. -) for each n ≥ 2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 33E
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Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (²1 n+1 (2) Use part (1) to compute the n-th partial sum sn. (3) Deduce that a 1 an converges and state its value. -) for each n > 2.
Transcribed Image Text:Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (²1 n+1 (2) Use part (1) to compute the n-th partial sum sn. (3) Deduce that a 1 an converges and state its value. -) for each n > 2.
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