(1) 由 a(n+2)=(3/2)a(n+1)-(1/2)an 知道:
a(n+2)-a(n+1)=(1/2)a(n+1)-(1/2)an
==> [a(n+2)-a(n+1)]/[a(n+1)-a(n)]=1/2
==> 即:d(n+1)/dn=1/2
==> {dn}是等比数列
(2) d1=1/2
于是:dn=(1/2)^(n-1)*d1
dn=(1/2)^n
==> an=d(n-1)+d(n-1)+d(n-2)+...+d2+d1
==> an=d1*[1-(1/2)^(n-1)]/[1-(1/2)]
==> an=1-1/2^n