Series expansion of logarithmic function

  • Thread starter seboastien
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  • #1
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Homework Statement


Find first three non zero terms in series expansion where the argument of funstion is small

ln(5+p)

Homework Equations





The Attempt at a Solution



The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to

(4+p)- 1/2(4+p)^2 + 1/3(4+p)^3 - .... however, I imagine that this would only work if p was approx -4.
 

Answers and Replies

  • #2
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Come on guys! I really need to know how to do this!
 
  • #3
HallsofIvy
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Homework Statement


Find first three non zero terms in series expansion where the argument of funstion is small

ln(5+p)

Homework Equations





The Attempt at a Solution



The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to

(4+p)- 1/2(4+p)^2 + 1/3(4+p)^3 - .... however, I imagine that this would only work if p was approx -4.
Well, the accuracy, for any finite polynomial expansion, deteriorates as p gets farther from -4 but is the accuracy really relevant? You are only asked to "Find first three non zero terms".
 
  • #4
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How do I find the first three non-zero terms of ln(5+p), I'm pretty sure that my answer is wrong.
 
  • #5
dynamicsolo
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You'll want to write this as ln( 5 [ 1+(p/5) ] ) ; then use the properties of logarithms to write it as two terms, one of which is the term you would do the series expansion for.
 
  • #6
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Thank you
 

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