数列满足Sn＝（n/2）×an Sn是前n项和 a2=1 求前n项和

易算得a1=0
S(n-1)=(n-1)a(n-1)/2
Sn-S(n-1)=[nan-(n-1)a(n-1)]/2=an
(n-2)an=(n-1)a(n-1)
an/a(n-1)=(n-1)/(n-2)
a(n-2)/a(n-3)=(n-2)/(n-3)
.....
a3/a2=2/1
累乘得an/a2=n-1
an=(n-1)
Sn=n(n-1)/2

S(2)=a(1)+a(2)=a(1)+1=a(2)=1,a(1)=0,

n>1时,
a(n)=S(n)-S(n-1)=n/2a(n) - (n-1)/2a(n-1),
(n-1)a(n-1) = (n-2)a(n)。

(n-1)/a(n) = (n-1 -1)/a(n-1) = (2 -1)/a(2) = 1,
a(n) = n-1, n = 1,2,...

S(n) = n/2a(n)=n(n-1)/2, n = 1,2,...