Solve Series Sequences: Find Constant Term

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Homework Help Overview

The discussion revolves around finding the constant term in the expansion of a given expression involving partial fractions. The subject area includes algebra and series expansions, particularly focusing on the manipulation of rational functions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss expressing the function in partial fractions and expanding it into a series. There are attempts to clarify the correct expression and the method to find the constant term. Some participants express confusion about the problem setup and seek further guidance.

Discussion Status

There is ongoing dialogue with some participants providing hints and partial guidance on how to approach the problem. However, explicit consensus on the method or solution has not been reached, and some participants are still seeking clarification on their understanding.

Contextual Notes

Participants note that there may have been confusion regarding the original question, leading to multiple clarifications. There are reminders about the forum's guidelines regarding homework help and the expectation for participants to engage in the problem-solving process rather than seeking direct solutions.

lovelife
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can anyone show me how to do this question ? thanks ...

express (1+x^2)/((1+x)(1+2x)) in partial fraction. (this step i know the solution )
hence,find the constant term in the expansion if (1+x^2)/(-3x(1+x)(1+2x)) in ascending power of x .( then this one don't know ,please help me ) thanks ...
 
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lovelife said:
can anyone show me how to do this question ? thanks ...

express (1+x^2)/((1+x)(1+2x)) in partial fraction. (this step i know the solution )
hence,find the constant term in the expansion if (1+x^2)/((1+x)(1+2x)) in ascending power of x .( then this one don't know ,please help me ) thanks ...

$$\frac{1+x^2}{(1+x)(1+2x)}=\frac{1}{2}-\frac{2}{1+x}+\frac{5}{2(1+2x)}=\frac{1}{2}-2(1-x+x^2-x^3+...)+\frac{5}{2}(1-2x+4x^2-8x^3+...)$$

so: what's the constant term of the above? Of course, you could know the answer without doing all the above...can you see how?

DonAntonio
 
er ... sorry ! i posted the wrong ques ...
actually is ...
hence ,find the constant term in the expansion if
(1+x^2)/(-3x(1+x)(1+2x)) in ascending power of x .
 
lovelife said:
er ... sorry ! i posted the wrong ques ...
actually is ...
hence ,find the constant term in the expansion if
(1+x^2)/(-3x(1+x)(1+2x)) in ascending power of x .


Yeah, some mistake, uh?! Really...Well, learn from the already given answer and deduce.

DonAntonio
 
sorry ! because i type the wrong ques ! could you show me again ! thanks ...
DonAntonio said:
$$\frac{1+x^2}{(1+x)(1+2x)}=\frac{1}{2}-\frac{2}{1+x}+\frac{5}{2(1+2x)}=\frac{1}{2}-2(1-x+x^2-x^3+...)+\frac{5}{2}(1-2x+4x^2-8x^3+...)$$

so: what's the constant term of the above? Of course, you could know the answer without doing all the above...can you see how?

DonAntonio
 
lovelife said:
sorry ! because i type the wrong ques ! could you show me again ! thanks ...


No, I won't. It is annoying people is so careless as to malwaste other people's time. Besides this you can use what I already answered!

DonAntonio
 
ok ! but anyway , thanks for your solution .
DonAntonio said:
No, I won't. It is annoying people is so careless as to malwaste other people's time. Besides this you can use what I already answered!

DonAntonio
 
Why "anyway"? You have been shown exactly HOW to do it. Apply the same idea to this problem- write as partial fractions, expand each fraction as a geoetric series, and "combine like terms".
 
because i want the step solution ! because i had do the one solution ,but teacher say the working are wrong !
HallsofIvy said:
Why "anyway"? You have been shown exactly HOW to do it. Apply the same idea to this problem- write as partial fractions, expand each fraction as a geoetric series, and "combine like terms".
 
  • #10
lovelife said:
because i want the step solution !
NO! That's not the way it works here at Physics Forums. Please read the rules (https://www.physicsforums.com/showthread.php?t=414380), especially the Homework Help Guidelines section. We are happy to help you work the problem, but we won't do your work for you.

Also, homework problems should be posted in the Homework & Coursework section, not in the math technical forums. I am moving this thread to that section.
lovelife said:
because i had do the one solution ,but teacher say the working are wrong !
 

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