# Representing a function as a power series

ReidMerrill

## Homework Statement

Represent the function (8x)/(6+x) as a power serioes f(x)=∑cnxn
Find
c0
c1
c2
c3
c4
Radius of convergence R=

## 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.

## Answers and Replies

Science Advisor
Homework Helper
Gold Member
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.

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

Science Advisor
Homework Helper
Gold Member
When I entered that it said I need to enter a number not a formula.
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.

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

Science Advisor
Homework Helper
Gold Member
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.

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

Science Advisor
Homework Helper
Gold Member
Well if the coefficient is meant to be 8/9 then it's still incorrect.
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?

Science Advisor
Homework Helper
Dearly Missed
When I entered that it said I need to enter a number not a formula. Of course x is a number in this case..

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##.