Partial Sums for Series: Solving Using Partial Fractions

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Homework Help Overview

The discussion revolves around the topic of series and partial sums, specifically focusing on the use of partial fractions to solve for terms in a series. Participants are examining the relationship between terms defined by the equation an = bn - bn+1.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the application of partial fractions to a specific equation and expressing confusion regarding the constants involved. There is a question about the next steps after determining the constants A and B. One participant suggests a potential typo in the original problem statement regarding the definition of an.

Discussion Status

The discussion is ongoing, with participants providing insights and clarifications about the steps involved in the problem. Some guidance has been offered regarding clearing denominators and solving for constants, but there is no explicit consensus on the next steps or the correctness of the original problem statement.

Contextual Notes

There is mention of a possible typo in the problem, which may affect the interpretation of the series being analyzed. Participants are also navigating the complexities of the equation provided and the implications of their findings.

gkamal
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Homework Statement


t5672v.jpg
[/B]

Homework Equations



an= bn - bn+1 which is already in the problem

The Attempt at a Solution


[/B]
i did partial fractions but then i got stuck at

16/12 [4n-5] - 16/12 [4n+7] that part about bn confuses me please someone explain in detail
 
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gkamal said:

Homework Statement


t5672v.jpg
[/B]

Homework Equations



an= bn - bn+1 which is already in the problem

The Attempt at a Solution


[/B]
i did partial fractions but then i got stuck at

16/12 [4n-5] - 16/12 [4n+7] that part about bn confuses me please someone explain in detail
Where's the equation you're working with?
Starting from ##\frac{16}{16n^2 + 8n - 35} = \frac{A}{4n - 5} + \frac{B}{4n + 7}##, multiply both sides by ##16n^2 + 8n - 35## to clear out all of the denominators. Then solve for the constants A and B.
 
i did and i get 16/12 for A and - 16/12 for B as i indicated above the problem is what is the next step
 
I think there's a typo in the problem. It should say ##a_n = b_n - b_{n+3}##.
 

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