高三数列题、求、已知首项为1的数列{an}的前n项和Sn满足 Sn+1/Sn=n+3/n+1求数列{an}的通项an
问题描述:
高三数列题、求、
已知首项为1的数列{an}的前n项和Sn满足 Sn+1/Sn=n+3/n+1
求数列{an}的通项an
答
Sn+1/Sn=n+3/n+1a(n+1)/Sn+1=(n+3)/(n+1)a(n+1)/sn=2/(n+1)得sn=(n+1)a(n+1)/2sn-1=nan/2相减的an=(1/2)[(n+1)a(n+1)-nan]2an+nan=(n+1)a(n+1)(2+n)an=(n+1)a(n+1)a(n+1)/an=(n+2)/(n+1)an/a(n-1)=(n+1)/n……………...