∵ln(1+x)=x-x^2/2+x^3/3-...+(-1)^(n+1)x^n/n+...
=∑(-1)^(n+1)x^n/n ,
据D'Alembert判别法=>lim(n->∞) n/(n+1)=1,
故该级数收敛半径为1,
又∵x≠ -1,
=> -1ln(1+(-x))=∑(-1)^(2n+1)x^n/n
= - ∑x^n/n,
∵x≠1,
=> -1≤x