=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2015)(1+1/2015) 每一项用平方差公式分解
=1/2 × 3/2×2/3 ×4/3×3/4 ×5/4×4/5 × ……× 2105/2014×2014/2015 ×2016/2015
=1/2×2016/2015
=1008/2015
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2015)(1+1/2015) 每一项用平方差公式分解
=1/2 × 3/2×2/3 ×4/3×3/4 ×5/4×4/5 × ……× 2105/2014×2014/2015 ×2016/2015
=1/2×2016/2015
=1008/2015