观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8

问题描述:

观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8
打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1

关键在于逆应用条件1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,由题意得(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x.x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(...