Taylor Series

  • Thread starter chemnoob.
  • Start date
  • #1
9
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Homework Statement


Obtain the Taylor series in powers of x + 1 for f(x) = x/(2 + x), giving
the general term.


Homework Equations





The Attempt at a Solution



Wrote it out as x*(1/1-(-(x+1)).
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
1,745
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If
[tex]
f(x)=\frac{x}{x+2}
[/tex]
We are asked to write it as a series in [tex]y=x+1[/tex], so in terms of y, the function becomes:
[tex]
F(y)=\frac{y-1}{y+1}
[/tex]
Now use all your previous knowledge about Taylor series to find the expansion in terms of y
 
  • #3
9
0
hmm.. confused
 
  • #4
hunt_mat
Homework Helper
1,745
26
OK, write your function as the following:
[tex]
f(x)=\frac{x}{x+2}=\frac{(x+1)-1}{(x+1)+1}
[/tex]
Use all the previous knowledge you have to find the taylor series.
 
  • #5
hunt_mat
Homework Helper
1,745
26
Or you could write:
[tex]
f(x)=\frac{x}{x+2}=\frac{x+2-2}{x+2}=1-\frac{2}{x+2}=1-\frac{2}{(x+1)+1}
[/tex]
If that makes it easier.
 

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