# Series sequences

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 ...

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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

Homework Helper
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".

Mentor
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 !