Question

求当n趋于无穷大时（n-1）^2/n+1的极限

求解 实在做不出来

Answer 1

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)^(1/x)=e 若是lim[n→∞] (n+1)²..