けんき says to YSITD
1/(1-t)=1+t+t^2+.. -log(1-t)=x+x^2/2+x^3/3.. (need check remainder converge) if -1<=x<1 then the series converge plug -x in log(1+x)=x-x^2/2+x^3/3-x^4/4+..