does this series converge or diverge? if converges enter the sum of the series. explain step by step
does this series converge or diverge? if converges enter the sum of the series. explain step by step
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 46E
Related questions
Question
does this series converge or diverge? if converges enter the sum of the series. explain step by step
Expert Solution
Step 1
The given series can be expanded as
(ln √2 - ln √1) + (ln √3 - ln √2) + (ln √4 - ln √3) + . . . . . . + ( ln √(n+1) - ln √n) + . . . . . .
= limn→∞ [ ln √(n+1) - ln √1 ]
= limn→∞ [ ln √(n+1) - 0 ]
Step by step
Solved in 2 steps
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