Power Series Expansion: Find Alternatives to Ʃ ((-1)^(i-1))/i

[venom192]

I posted this in the homework section, but it's not a homework problem.

I basically need to know if the series Ʃ ((-1)^(i-1))/i can be represented in other ways (e.g. a Taylor series, but I doubt it). I know it converges to ln2, but I need to know if there's a series like x^2, x^4, ... or something like it that I can represent it with.

 

[pwsnafu]

I posted this in the homework section, but it's not a homework problem.

I basically need to know if the series Ʃ ((-1)^(i-1))/i can be represented in other ways (e.g. a Taylor series, but I doubt it). I know it converges to ln2, but I need to know if there's a series like x^2, x^4, ... or something like it that I can represent it with.

Do you know the Taylor series for $\log (x+1)$ ?