# Thread: Expand in a power series

1. ## Expand in a power series

Split : $\frac{1}{(x+1)(x+2)}$ into partial fractions and hence expand the expression in power series in x up to to the term in $x^3$ What is the term in $x^5$?

The expression in partial fractions is $\frac{1}{x+1}-\frac{1}{x+2}$ However, I don't know how to expand it in power series.

2. Originally Posted by Boz
Split : $\frac{1}{(x+1)(x+2)}$ into partial fractions and hence expand the expression in power series in x up to to the term in $x^3$ What is the term in $x^5$?

The expression in partial fractions is $\frac{1}{x+1}-\frac{1}{x+2}$ However, I don't know how to expand it in power series.
Note that the can be rewritten as

$\displaystyle \frac{1}{x+1}=\frac{1}{1-(-x)}$ and the 2nd is

$\displaystyle \frac{-1}{x+2}=\frac{-1}{2}\frac{1}{1+\frac{x}{2}}=\frac{-1}{2}\frac{1}{1-\frac{-x}{2}}$

Both of these are geometric series. Now just find $r$. Can you finish from here?

3. Originally Posted by TheEmptySet
Note that the can be rewritten as

$\displaystyle \frac{1}{x+1}=\frac{1}{1-(-x)}$ and the 2nd is

$\displaystyle \frac{-1}{x+2}=\frac{-1}{2}\frac{1}{1+\frac{x}{2}}=\frac{-1}{2}\frac{1}{1-\frac{-x}{2}}$

Both of these are geometric series. Now just find $r$. Can you finish from here?
No. Could you write me the full solution, please.
I haven't started the series topic yet, because I have an exam on AC circuits next week and Im freaking out!

4. No I will not. If you are an EE you should know this stuff. I walked you to the answer. If you would do a simple google search you might find this
Geometric series - Wikipedia, the free encyclopedia
with what i said above you can solve the question.

5. Originally Posted by TheEmptySet
No I will not. If you are an EE you should know this stuff. I walked you to the answer. If you would do a simple google search you might find this
Geometric series - Wikipedia, the free encyclopedia
with what i said above you can solve the question.
No,I am 1st year Mech Eng student. I havent had the time recently to sit and work on these problems I said why. Im gonna try to solve the series problem now because I have to submit it tomorrow.

6. Originally Posted by Boz
No,I am 1st year Mech Eng student. I havent had the time recently to sit and work on these problems I said why. Im gonna try to solve the series problem now because I have to submit it tomorrow.
Did you look at the link? If you did it SHOWS you the answer. If I write them down(I solved the problem ) and you turn them in for credit that is plagerism. YOU are responsible for understanding the material. Geometric series are covered in most college algebra classes and then again in depth in Calculus. You need to show some work.

7. Originally Posted by Boz
No,I am 1st year Mech Eng student. I havent had the time recently to sit and work on these problems I said why. Im gonna try to solve the series problem now because I have to submit it tomorrow.
Thread closed as the implication of the above is that it is part of your assessment.

PM if you can justify that things are otherwise.

(Also look at the earlier posts, you have been given everything you need (line 11 after "Formula") to do this problem short of TheEmptySet typing out what is on the link he gave again)

CB