Taylor Series for ln(1-3x) about x = 0 | Homework Question

[ganondorf29]

Homework Statement

Determine the Taylor Series for f(x) = ln(1-3x) about x = 0

Homework Equations

ln(1+x) = \sum\fract(-1)^n^+^1 x^n /{n}

The Attempt at a Solution

ln(1-3x) = ln(1+(-3x))

ln(1+(-3x)) = \sum\fract(-1)^n^+^2 x^3^n /{n}

Is that right?

 

[Wretchosoft]

The -1 is in the right place, but I'm not sure why the 3 migrated to the exponent.

 

[ganondorf29]

So is it:
<br /> \sum\fract(-1)^n^+^2 3x^n /{n}<br />

 

[e(ho0n3]

You check it yourself by computing the first couple of terms in the Taylor series.