# Representing a function as a power series

1. Apr 11, 2016

### ReidMerrill

1. The problem statement, all variables and given/known data
Represent the function (8x)/(6+x) as a power serioes f(x)=∑cnxn
Find
c0
c1
c2
c3
c4

2. Relevant equations

3. The attempt at a solution
I've represented this function as (8x/9)∑(-x/6)n
and found I-x/6I <1 so R=6

Through pure guessing I discovered c0=0 but I don't really know where cn and xn are in this series.

2. Apr 11, 2016

### andrewkirk

Write out the first few terms of the expression you got, without the summation sign $\sum$. The coefficients of $x,x^2,x^3,x^4$ are $c_1,c_2,c_3,c_4$ respectively.

3. Apr 11, 2016

### ReidMerrill

When I entered that it said I need to enter a number not a formula. Of course x is a number in this case..

4. Apr 11, 2016

### andrewkirk

The coefficients are numbers. The powers of $x$ are not part of the coefficient. Punch the (purely numeric) formula for each coefficient through your calculator to get a decimal number to submit to your online assignment-marking system.

5. Apr 11, 2016

### ReidMerrill

I don't understand. There is no part of the series that doesn't have x in it.

6. Apr 11, 2016

### andrewkirk

To understand the solution it's necessary to understand what a coefficient is. Read the introduction to this wiki article, then reread the posts above and you should be able to understand them.

7. Apr 11, 2016

### ReidMerrill

Well if the coefficient is meant to be 8/9 then it's still incorrect.

8. Apr 11, 2016

### andrewkirk

Even if the formula in the OP were correct, none of the coefficients would be 8/9.
Further, the formula in the OP is not correct. Where did the 9 come from?

9. Apr 12, 2016

### Ray Vickson

No: you are being asked to write the series as $c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \cdots$, where $x$ is the variable and $c_0, c_1, c_2, c_3, \ldots$ are some constants. You are being asked to determine the values of $c_0, c_1, c_2, c_3, \ldots$.