观察式子(1-1/2²)(1-1/3²）=(1-1/2)(1+1/2)(1-1/3)(1+1/3)=1/2x3_数学解答

观察式子(1-1/2²)(1-1/3²）=(1-1/2)(1+1/2)(1-1/3)(1+1/3)=1/2x3/2x2/3x4/3=2/3试求
试求(1-1/2²）(1-1/3²)x…x(1-1/2009²)(1-1/2010²）的值

人气：466 ℃　时间：2020-01-25 05:44:23

解答

(1-1/2²）(1-1/3²)x…x(1-1/2009²)(1-1/2010²）=(1-1/2)(1+1/2)(1-1/3)(1+1/3)x……x(1-1/2010)(1+1/2010)=1/2x3/2x2/3x4/3x……x2011/2010=1/2x2011/2010=2011/4020