Sn=[(1+An)/2]^2 求An的通项公式

A1=1
Sn = Sn=[(1+An)/2]^2
S(n-1) =[(1+A(n-1))/2]^2
然后减一下得到
An = [An^2 +2An - A(n-1)^2 - 2A(n-1)]/4
化简得到(An - 1)^2 = (A(n-1) +1)^2
An = A(n-1) +2
An = 2n-1

daan