(1-1⼀2^2)(1-1⼀3^2)(1-1⼀4^2).........(1-1⼀n^2)

2025-02-25 01:11:40
推荐回答(1个)
回答1:

用平方差分解,然后消去中间全部互为倒数的部分:

(1-1/2^2)(1-1/3^2)(1-1/4^2).........(1-1/n^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)```(1-1/n)(1+1/n)
=(1/2)(3/2)(2/3)(4/3)```((n-1)/n)((n+1)/n)
=(1/2)((n+1)/n)
=(n+1)/2n