搜搜做题作业网希望大神解答,谢谢.
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/06/16 11:19:59
希望大神解答,谢谢.
（1）3/4
(2)2/3
(3)5/8
（1-1/2²)(1-1/3²)(1-1/4²)...(1-1/9²)(1-1/10²)...(1-1/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/n)(1+1/n)
=1/2×3/2×2/3×4/3×3/4×5/4×...×(n-1)/n·(n+1)/n
=1/2×(n+1)/n
=(n+1)/2n
(2)2/3
(3)5/8
（1-1/2²)(1-1/3²)(1-1/4²)...(1-1/9²)(1-1/10²)...(1-1/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/n)(1+1/n)
=1/2×3/2×2/3×4/3×3/4×5/4×...×(n-1)/n·(n+1)/n
=1/2×(n+1)/n
=(n+1)/2n