a(2k+1)/a(2k-1)=(k+1)/ka(2k-1)/a(2k-3)=k/(k-1)…………a3/a1=2/1连乘a(2k+1)/a1=[2×3×...×(k+1)]/(1×2×3×...×k)=k+1a(2k+1)=a1(k+1)=k+1(2011-1)/2=1005 k=1005a2011=1005+1=1006