求当n趋向无限大时lim[(n+1)^2/(n-1)]的极限?
问题描述：
求当n趋向无限大时lim[(n+1)^2/(n-1)]的极限?
答
你应该是问lim[n→∞] (n+1)^[2/(n-1)]吧?=lim[n→∞] (1+n)^[1/n·2n/(n-1)]=1^lim[n→∞] 2n/(n-1)=1^lim[n→∞] 2/(1-1/n),上下除n=1^[2/(1-0)]=1这里运用了lim[x→∞] (1+x)^(1/x)=1而不同于这lim[x→0] (1+x)^(...