Solve Series Sequences: Find Constant Term

[lovelife]

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 ...

 

[DonAntonio]

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

 

[lovelife]

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 .

 

[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 .

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

DonAntonio

 

[lovelife]

sorry ! because i type the wrong ques ! could you show me again ! 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

 

[DonAntonio]

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

 

[lovelife]

ok ! but anyway , thanks for your solution .

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

 

[HallsofIvy]

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".

 

[lovelife]

because i want the step solution ! because i had do the one solution ,but teacher say the working are wrong !

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".

 

[Mark44]

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.

because i had do the one solution ,but teacher say the working are wrong !