a1=1,a2=2,an+2=(an+an-1)/2,n∈N+,(1)令bn=an+1-an,证明bn是等比数列
问题描述：
a1=1,a2=2,an+2=(an+an-1)/2,n∈N+,(1)令bn=an+1-an,证明bn是等比数列
答
a(n+2)=[an十a(n+1)]/2=a(n+2)-a(n+1)=[an-a(n+1)]/2
化b(n+1)=-1/2*bn(因bn=a(n+1)-an)
{bn}等比数列,b1=1,公比-1/2
则bn=(-1/2)^(n-1)