应用平方差公式展开=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2011)(1+1/2011)=1/2× 3/2×2/3 × 4/3×3/4× 5/4×4/5×……×2010/2011 ×2012/2011=1/2×2012/2011=1006/2011