1+1/2+1/4+1/8+1/16+1/32+1/64

1+1/2+1/4+1/8+1/16+1/32+1/64
1+1/2+1/4+1/8+1/16+1/32+1/64

1+1/2+1/4+1/8+1/16+1/32+1/64
1+1/2+1/4+1/8+1/16+1/32+1/64
=(1+1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/64
=(1+1/2+1/4+1/8+1/16+1/32+1/32)-1/64
=(1+1/2+1/4+1/8+1/16+1/16)-1/64
=...
=1+1-1/64
=2-1/64
=1又53/64

?

设原式=x=1+1/2+1/4+1/8+1/16+1/32+1/64
2x=2+1+1/2+....+1/32
则：原式=2x-x=(2+1+1/2+...+1/32)-(1+1/2+1/4+...+1/64)
=2-1/64
=1又63/64

1+1/2+1/4+1/8+1/16+1/32+1/64=1+63/64=127/64

1+1/2+1/4+1/8+1/16+1/32+1/64
=1(1-1/64)/(1-1/2)=63/32;

先化简，最大的分母是64，所以将各项化为64为分母的分数
那么就是64/64+32/64+16/64+8/64+4/64+2/64+1/64
然后化简 =127/64

这是个等比数列，公比1/2
1+1/2+1/4+1/8+1/16+1/32+1/64
=1+(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)
=2-1/64
=1+63/64
=1又63/64