(1-1⼀2^2)(1-1⼀3^2)(1-1⼀4^2)…(1-1⼀10^2)…(1-1⼀n^2)用简便的方法计算出来，初二数学？谢了啊，再把规...

(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/10^2)…(1-1/n^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)(1-1/5)(1+1/5)(.....)(1-1/n)(1+1/n)
=1/2×3/2×2/3×4/3×3/4×....(1+1/n)
=1/2(1+1/n)
=1/2+1/2n

(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/10^2)…(1-1/n^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)(1-1/5)(1+1/5)(.....)(1-1/n)(1+1/n)
=(1-1/2)(1-1/3)(1-1/4)(1-1/5)...(1-1/n) (1+1/2)(1+1/3)(1+1/4)(1+1/5)...(1+1/n)
=1/2 * 2/3 * 3/4*..*(n-1)/n* 3/2 * 4/3 * 5/4 *...* (n+1)/n
约分得
=1/n * (n+1)/2
=(n+1)/2n

原式=【(1-1/2)（1+1/2）】【(1-1/3)（1+1/3）】……【（1-1/n）(1+1/n)】
=【(1-1/2)(1-1/3)……(1-1/n)】【(1+1/2)(1+1/3)……(1+1/n)】
=【1/2*2/3*3/4*……*（n-2）/（n-1）*(n-1)/n】【3/2*4/3*5/4……*n/（n-1）*（n+1）/n】
=1/n*(n+1)/2
=(n+1)/2n