1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Representing a function as a power series

  1. Apr 11, 2016 #1
    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
    Radius of convergence R=

    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. jcsd
  3. Apr 11, 2016 #2

    andrewkirk

    User Avatar
    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.
     
  4. Apr 11, 2016 #3
    When I entered that it said I need to enter a number not a formula. Of course x is a number in this case..
     
  5. Apr 11, 2016 #4

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  6. Apr 11, 2016 #5
    I don't understand. There is no part of the series that doesn't have x in it.
     
  7. Apr 11, 2016 #6

    andrewkirk

    User Avatar
    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.:smile:
     
  8. Apr 11, 2016 #7
    Well if the coefficient is meant to be 8/9 then it's still incorrect.
     
  9. Apr 11, 2016 #8

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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?
     
  10. Apr 12, 2016 #9

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Representing a function as a power series
Loading...