Power Series of Logs: Solving f(x)=x2ln(1-x)

[jkim91@vt.edu]

First post! I'm having a lot of trouble with power series, especially when there's more than one of the same variable in a function.

Find the first few terms of the power series for the function
f(x)=x²ln(1-x)


I did a taylor series expansion of it, which gave me the right answer, but the work took forever. I figure power series would be a lot easier.

 

[lanedance]

I'm not too sure what you're asking? a taylor series is a power series around x=0

one way that could be quicker here though, is to find the series for ln(1-x) then multiply it by x^2