# Series expansion of logarithmic function

## Homework Statement

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

ln(5+p)

## 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.

Come on guys! I really need to know how to do this!

HallsofIvy
Homework Helper

## Homework Statement

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

ln(5+p)

## 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".

How do I find the first three non-zero terms of ln(5+p), I'm pretty sure that my answer is wrong.

dynamicsolo
Homework Helper
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.

Thank you