计算:(1-1⼀2^2)(1-1⼀3^2)(1-4^2)(1-1⼀5^2)···(1-1⼀9^2)(1-1⼀10^2) 急~~~~~~~

2025-02-23 22:39:27
推荐回答(2个)
回答1:

用平方差
(1-1/2^2)(1-1/3^2)(1-4^2)(1-1/5^2)···(1-1/9^2)(1-1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
=(1/2)(11/10)
=11/20

回答2:

1-1/n²=(n-1)/n*(n+1)/n

原式=(1/2)*(3/2)*(2/3)*(4/3)…… (9/10)*(11/10)

=(1/2)*(11/10)

=11/20