已知数列an是等比数列,前三项为a,1/2a+1/2,1/3a+1/3.数列前n项和为Sn,求lim Sn.
问题描述：
已知数列an是等比数列,前三项为a,1/2a+1/2,1/3a+1/3.数列前n项和为Sn,求lim Sn.
答
(1/2a+1/2)^2=a*(1/3a+1/3)1/4(1/a+1)^2=1/3*a*(1/a+1)1/4(1/a+1)=1/3*a3(1/a+1)=4a3(1+a)=4a^24a^2-3a-3=0等比数列[1/2(a+1)]^2=a*[1/3(a+1)]1/4*(a+1)^2=a/3*(a+1)等比数列的项不等于0a+1不等于0所以(a+1)/4=a/3a=...