用ε-Ν定义证明lim(1-n)/(1+n)=-1,n趋向于无穷大

设ε是已知的任小的数lim(1-n)/(1+n)=lim[-1+2/(n+1)]由于lim[-1+2/(n+1)]-（-1）=lim（2/(n+1)）令lim（2/(n+1)）-ε ①由于n趋向于无穷大所以当n大于/2ε-1时不等式①总小于0。也就是说lim[-1+2/(n+1)]-（-1）=0即lim(1-n)/(1+n)=-1