Question

1/2+1/4+1/8+1/16+1/32+1/64+1/128的巧算

Answer 1

=127/128
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/128
因为每一项后面的分母都是前面的一半,所以你可以在原来的式子最后+1/128,可以发现从后往前算,就是2个1/128加起来变成1个1/64,然后2个1/64加起来变成1个1/32,依次类推

Answer 2

将分母同时化成128，然后在分子进行简单的加运算，最后约分就可以了

Answer 3

1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)-1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/128
=1-1/128
=127/128

Answer 4

1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)+(1/64-1/128)
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
=1-1/128
=127/128