Solve Series Sequences: Find Constant Term

In summary, solving series sequences involves finding a constant term, which is a fixed value that remains the same throughout the sequence. This constant term can be found by identifying the pattern or rule within the sequence and using it to calculate the value of the constant term. Once the constant term is determined, it can be used to predict future terms in the series and understand the overall behavior of the sequence.
  • #1
lovelife
5
0
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 ...
 
Last edited:
Physics news on Phys.org
  • #2
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
 
  • #3
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 .
 
  • #4
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
 
  • #5
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
 
  • #6
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
 
  • #7
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
 
  • #8
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".
 
  • #9
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 !
 

FAQ: Solve Series Sequences: Find Constant Term

What is a series sequence?

A series sequence is a set of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.

How do you find the constant term in a series sequence?

The constant term in a series sequence is the number that remains the same throughout the entire sequence. To find it, you can look for any pattern in the series and determine which number is repeating or staying constant.

What is the formula for finding the constant term in a series sequence?

The formula for finding the constant term in a series sequence is C = a + (n-1)d, where C is the constant term, a is the first term in the sequence, n is the number of terms, and d is the common difference between consecutive terms.

Can you give an example of finding the constant term in a series sequence?

For example, if you have a sequence with the first term of 3 and a common difference of 5, the constant term would be 3 since it remains the same throughout the sequence. Using the formula, C = 3 + (n-1)5, if n is 5 (the number of terms), then the constant term would be 3 + (5-1)5 = 3 + 4(5) = 23.

Why is it important to find the constant term in a series sequence?

Finding the constant term in a series sequence can help you understand the pattern and predict future terms in the sequence. It also allows you to calculate the sum of the series and determine if the series is convergent or divergent.

Similar threads

Find the ##r^{th}## term of ##(a+2x)^n##
Replies
3
Views
1K
Show that if ##x>1##, ##\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-##
Replies
8
Views
1K
Values of x for which a geometric series converges
Replies
1
Views
4K
Find the nth term of the given sequence
Replies
7
Views
1K
Straight line intersects geometric sequence
Replies
5
Views
1K
Question about this technique for solving simultaneous equations
Replies
4
Views
1K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
1K
Solving a nested logarithmic equation
Replies
2
Views
1K
How to Solve Arithmetic Sequence Problems
Replies
1
Views
1K
To find the range of a given ##\sin## function
Replies
15
Views
1K

Hot Threads

Recent Insights

Back
Top