计算:(1-1/2)(1/3-1)(1-1/4)(1/5-1)……(1-1/2010)(1/2011-1)

问题描述:

计算:(1-1/2)(1/3-1)(1-1/4)(1/5-1)……(1-1/2010)(1/2011-1)


原式
=1/2x(-2/3)x3/4x(-4/5)x……x2009/2010x(-2010/2011)
=1/2x2/3x3/4x4/5x……x2009/2010x2010/2011 (偶数个负相乘为正)
=1/2011 (中间约分全部抵消了)