(1-1⼀2^2)(1⼀3^2)(1⼀4^2)......(1-1⼀10^2) 用因式分解简便运算

2024-12-18 17:48:48
推荐回答(1个)
回答1:

(1-1/2^2) = (2^2 - 1) / 2^2 = (2-1)*(2+1) /2^2 = 1*3/2^2
(1-1/3^2) = (3^2 - 1) / 3^2 = (3-1)*(3+1) /3^2 = 2*4/3^2
(1-1/4^2) = (4^2 - 1) / 4^2 = (4-1)*(4+1) /4^2 = 3*5/4^2
......
(1-1/2^2) (1-1/3^2) * ...... * (1-1/10^2)
= [(1*3) (2*4) (3*5) (4*6) (5*7) (6*8) (7*9) (8*10) (9*11) ] / [ (2*3*4* ...... * 10)^2]
= ( 1*2*10*11) / ( 2^2 * 10^2 )
= 11/20