设数列an的前n项和为Sn,a1=1 ,an = 2Sn²/2Sn-1 (n≥2)

问题描述:

设数列an的前n项和为Sn,a1=1 ,an = 2Sn²/2Sn-1 (n≥2)
(1)求数列1/Sn的前n项和Tn.
(2)求通项公式an

其实很简单 还是用公式 an = Sn-S(n-1)2Sn²/(2Sn-1) = an = Sn- Sn-1 → S(n-1) = Sn - 2Sn²/(2Sn-1) = -Sn/(2Sn-1)分子分母颠倒 1/S(n-1) = 1/Sn - 2于是 1/Sn = 1/S(n-1) +21/Sn 是以1 为首项,2为公差的...