（数后33 2）在等比数列{an}中，a1=2,前n项和为Sn,若数列{an+1}也是等比数列，则Sn等于

显示全部楼层 · 2012-2-16 13:37:36

设公比为q,a22=a1*a3(a2+1)2=(a1+1)(a3+1)因为a1=2所以a22=2a3(a2+1)2=3(a3+1)解得a2=2a3=2所以sn=2×n=2n....

千问 · 2012-2-16 13:37:36

an+1=aq^(n-1)+1a(n+1)+1=aq^(n)+1a(n+2)+1=aq^(n+1)+1(aq^(n)+1)^2=(aq^(n-1)+1)(aq^(n+1)+1)a^2*q^(2n)+2aq^n+1=a^2*q^(2n)+aq^(n+1)+aq^(n-1)+12q^n=q^(n+1)+q^(n-1)q^(n-1)(q^2...

千问 · 2012-2-16 13:37:36

(a2+1)2=(a1+1)(a3+1)a1=2,设an公比q(2q+1)2=3(2q2+1)4q2+4q+1=6q2+32q2-4q+2=0q=1所以an=a1=2Sn=2n...