求lim(Sn+Sn+1)/(Sn+Sn-1),an为等差数列,a1不为零
问题描述：
求lim(Sn+Sn+1)/(Sn+Sn-1),an为等差数列,a1不为零
答
设sn=a1+(n-1)d,则sn=a1*n+n(n-1)d/2代入lim(Sn+Sn+1)/(Sn+Sn-1)=[na1+n(n-1)d/2+（n+1）*a1+n^2d]/[na1+n(n-1)d/2+（n-1）a1+(n-2)(n-1）d/2]上下同时除以n^2得=lim[1/na1+(1-1/n)d/2+（1/n+1/n^2）*a1+d]/[1/na1+(...