问题标题:
高二无穷数列极限{an}是等差数列,Sn为数列前n项和(a1≠0)求:(1)limn→∞(nan)/Sn(2)求limn→∞Sn+Sn+1/Sn+Sn-1(n+1和n-1是角标)第1题我做好了,是2,
问题描述:
高二无穷数列极限
{an}是等差数列,Sn为数列前n项和(a1≠0)
求:(1)limn→∞(nan)/Sn
(2)求limn→∞Sn+Sn+1/Sn+Sn-1(n+1和n-1是角标)
第1题我做好了,是2,
郭 阳回答:
假设an=a1+(n-1)d则sn=na1+(n^2-n)d/2sn+sn+1=(2n+1)a1+n^2*dsn+sn-1=2na1+(n^2-n+1)*dsn+sn+1/sn+sn-1=(2n+1)a1+n^2*d/2na1+(n^2-n+1)*d分子分母同时除以n^2可以变为:[(2/n+1/n^2)a1+d]/[2/n*a1+(1-1/n+1/n^2)]当N...
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