part 1 (ii) Course : Real Analysis

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 28E
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part 1 (ii) Course : Real Analysis

Question 1
Prove the limit comparison theorem
i. Suppose that an20 and b,20 and that
an
lim
7=
and Eb, both converge or both diverge.
2n2 +n+2
Then either En=an
i Use the result in (i) to test for convergence Zn=1
5n3 + 3n
1
iii. Use the result in (i) to test for convergence 2, =1
3D1
Vn? + 5
Transcribed Image Text:Question 1 Prove the limit comparison theorem i. Suppose that an20 and b,20 and that an lim 7= and Eb, both converge or both diverge. 2n2 +n+2 Then either En=an i Use the result in (i) to test for convergence Zn=1 5n3 + 3n 1 iii. Use the result in (i) to test for convergence 2, =1 3D1 Vn? + 5
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