Question

(1/2)*(1+(1/2))*(1+(1/4))*(1+(1/16))*(1+(1/32) 简便算法，速度解答，谢谢

大神们,那个对？？？

Answer 1

把1/2换成1-1/2,值不变
反复利用平方差公式

原式=(1-1/2)(1+1/2)*(1+1/4)*(1+1/16)(1+1/32)
=(1-1/4)(1+1/4)*(1+1/16)*(1+1/32)
=(1-1/16)(1+1/16)*(1+1/32)
=(1-1/256)*33/32
=255/256*33/32
=8415/8192

如果题目像你写的那样,我的对
如果是楼上那朋友改了的那样,他的对

Answer 2

数字有误，修改了：
(1/2)*(1+(1/2))*(1+(1/4))*(1+(1/16))*(1+(1/256))

=（(1-1/2)*(1+(1/2))*(1+(1/4))*(1+(1/16))*(1+(1/256))
=（1-1/4）*(1+(1/4))*(1+(1/16))*(1+(1/256))
=（1-1/16 ）*(1+(1/16))*(1+(1/256))
=（1-1/256）（1+1/256)
=1-1/65536
=65535/65536