Question

急急急！（1-1/4）*（1-1/9）*（1-1/16）*（1-1/25）·····（1-1/64）有简便方法吗？

Answer 1

式子是1-（1/n^2）=(1-1/2)(1+1/2)
（1-1/4）*（1-1/9）*（1-1/16）*（1-1/25）·····（1-1/64）
= (1-1/2)(1+1/2) (1-1/3)(1+1/3) (1-1/4)(1+1/4) (1-1/5)(1+1/5) (1-1/6)(1+1/6) (1-1/7)(1+1/7) (1-1/8)(1+1/8)
=1/2 *3/2 * 2/3 * 4/3 *3/4* 4/5 * 4/5 *6/5 * 5/6 * 6/7 *6/7 8/7 * 7/8 * 9/8
=1/2*(3/2 * 2/3 )* (4/3 *3/4)* (4/5 * 4/5) *(6/5 * 5/6) *( 6/7 *6/7 )*( 8/7 * 7/8) * 9/8
=1/2*1*1*1*1*1*1*9/8
=9/16

Answer 2

（1-1/4）*（1-1/9）*（1-1/16）*（1-1/25）·····（1-1/64）
=3/4*8/9*15/16*24/25*35/36*48/49*63/64
=(3*8*15*24*35*48*63)/(4*9*16*25*36*49*64)
=(8*9*25*7*8*6*7*9)/(8*9*8*25*7*7*4*9*64)
=6/(4*64)
=3/128