已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2 ①求证1已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2①求证1/Sn是否为等差数列②求Sn和an

已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2 ①求证1已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2①求证1/Sn是否为等差数列②求Sn和an
已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2 ①求证1
已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2
①求证1/Sn是否为等差数列②求Sn和an

已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2 ①求证1已知数列an的前n项和为Sn,且满足 a1=1/2,An=-2SnS(n-1) n>=2①求证1/Sn是否为等差数列②求Sn和an
an=sn-s(n-1)
sn-s(n-1)+2sns(n-1)=0
1/sn-1/s(n-1)=(s(n-1)-sn)/sns(n-1)=2
所以,数列{1/sn}是等差数列,公差是2.
首项是1/S1=1/a1=2
所以,sn=2+(n-1)*2=2n
an=sn-s(n-1)=2n-2(n-1)=2