Question

Use the series for f(x)=1/(1-x) to write the series for g(x)=Ln|1-x|

a) C+ Ln|1+ x + x^2 + x^3+......|
b) C+ 2+ 2x+ 3x^2
c) C+ x+ x^2/2 +x^3/3
d) None of these

Note: you said since ln(1-x)= integral dx/(1-x) and integrate the taylor series for 1/(1-x). How can I do this???? This is my last exercise to submit my assigment. Please help me pleaseeeee

Answer 1

1/(1-x) = 1+x+x^2+x^3+x^4+...
so,
ln(1-x) = ∫(1+x+x^2+x^3+x^4+...) dx
= x + x^2/2 + x^3/3 + x^4/4 + ...

Answer 2

oops. Forgot the minus sign
∫1/(1-x) dx = -ln(1-x)
so the series is all negative terms.
But I'm sure you caught that ...

Answer 3

so will be the answer C??????