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Representing a function as a power series

  • #1

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=

Homework Equations




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

  • #2
andrewkirk
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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
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..
 
  • #4
andrewkirk
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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.
 
  • #5
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.
 
  • #6
andrewkirk
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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.:smile:
 
  • #7
Well if the coefficient is meant to be 8/9 then it's still incorrect.
 
  • #8
andrewkirk
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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?
 
  • #9
Ray Vickson
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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##.
 

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