早教吧作业答案频道 -->数学-->
(1-1/4)x(1-1/9)x(1-1/16)x...x(1-1/100)
题目详情
(1-1/4)x(1-1/9)x(1-1/16)x...x(1-1/100)
▼优质解答
答案和解析
(1-1/4)x(1-1/9)x(1-1/16)x...x(1-1/100)
=(1-1/2²)x(1-1/3²)x(1-1/4²)x...x(1-1/10²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4) .(1+1/10)(1-1/10)
=(1+1/2)(1+1/3)(1+1/4).(1+1/10) ×(1-1/2)(1-1/3).(1-1/10)
=3/2*4/3*5/4*.*11/10 ×1/2*2/3*3/4*.*9/10
=11/2 ×1/10
=11/20
=(1-1/2²)x(1-1/3²)x(1-1/4²)x...x(1-1/10²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4) .(1+1/10)(1-1/10)
=(1+1/2)(1+1/3)(1+1/4).(1+1/10) ×(1-1/2)(1-1/3).(1-1/10)
=3/2*4/3*5/4*.*11/10 ×1/2*2/3*3/4*.*9/10
=11/2 ×1/10
=11/20
看了 (1-1/4)x(1-1/9...的网友还看了以下：