a.
To find: if a series is convergent by the Integral Test, how do estimate its sum.
a.
Answer to Problem 7RCC
Explanation of Solution
Given information:
Calculation:
If the given series is
Then let
As for the partial sum, can find it by adding the first few terms, the number of how many term add.
Is determined from the Reminder Theorem:
From the above, reach an estimate on the sum which is :
b.
To find: if a series is convergent by the Comparison Test, how do estimate its sum.
b.
Answer to Problem 7RCC
Explanation of Solution
Given information:
Calculation:
Recall the Comparison test for Convergence:
If have the series
If
Then
It follows simple logic then, that:
Now the reminder of
And the reminder of
Same logic shown above gives:
c.
To find: if a series is convergent by the Alternative Series Test, how do estimate its sum.
c.
Answer to Problem 7RCC
Explanation of Solution
Given information:
Calculation:
Recall the
If have the series:
If:
The series Converges:
The Alternate Series Estimation Theorem states for the sum:
Where
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning