n≥2时,
an=2Sn²/(2Sn -1)
Sn -S(n-1)=2Sn²/(2Sn -1)
2Sn²-Sn -2SnS(n-1)+S(n-1)=2Sn²
S(n-1) -Sn=2SnS(n-1)
等式两边同除以SnS(n-1)
1/Sn -1/S(n-1)=2,为定值.
1/S1=1/a1=1/1=1
数列{1/Sn}是以1为首项,1为公差的等差数列.
1/Sn=1+1×(n-1)=n
Sn=1/n