任给ε>0,要使│(n^2+1)/(n^2-1)-1│<ε,即│2/(n^2-1)│<εn^2-1>2/ε，∴N=[√(1+2/ε)]所以，任给ε>0,都存在自然数N=[√(1+2/ε)]，使当n>N时，│(n^2+1)/(n^2-1)-1│<ε根据极限定义，得 lim（n趋向于无穷）[(n^2+1)/(n^2-1)]=1
