Question

已知数列an,a1=1,当n大于等于2时,其前n项和满足sn＾2=an(sn-1/2).求sn的表达式

Answer 1

s²n=(sn-s(n-1))(sn-1/2)

s²n=s²n-sn/2-s(n-1)*sn+s(n-1)/2

sn(1/2+s(n-1))=s(n-1)/2

sn=s(n-1)/(1+2s(n-1))

1/sn=(1+2s(n-1))/s(n-1)

1/sn=1/s(n-1)+2

1/sn=1/a1+2(n-1)

1/sn=2n-1

sn=1/(2n-1)