(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)

问题描述:

(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)

解;
原式=(1-1/10)(1+1/10)*(1-1/11)(1+1/11)*……*(1-1/100)(1+1/100)
=9/10*11/10*10/11*12/11*…………*99/100*101/100
=1/10*101/100
=101/1000你错了是9*101/1000恩恩,sorry解;原式=(1-1/10)(1+1/10)*(1-1/11)(1+1/11)*……*(1-1/100)(1+1/100)=9/10*11/10*10/11*12/11*…………*99/100*101/100=9/10*101/100=909/1000