数列{an}满足a1=1,an^2=(2an+1)a(n+1),令bn=lg(1+1/an),求证{bn}为等比数列
问题描述:
数列{an}满足a1=1,an^2=(2an+1)a(n+1),令bn=lg(1+1/an),求证{bn}为等比数列
求{an}通项公式
求证 ∑(ai/(1+ai))
答
an^2=(2an+1)a(n+1),a(n+1)=an²/(2an+1) (1)a(n+1)+1=an²/(2an+1)+1=(an+1)²/(2an+1) (2)(2)÷(1) [a(n+1)+1]/a(n+1)=[(an+1)/an]²依次顺推)(an+1)/an={[a(n-1)+1]/a(n-1)}²=.=[(a1+1)/a1]...“