1/2+1/4+1/8+1/16+.+1/512快

1/2+1/4+1/8+1/16+.+1/512快
1/2+1/4+1/8+1/16+.+1/512
快

1/2+1/4+1/8+1/16+.+1/512快
1/2+1/4+1/8+1/16+.+1/512
=1/2+1/2-1/4+1/4-1/8.+1/256-1/512
=1/2+1/2-1/512
=511/512

1/2+1/4=3/4
3/4+1/8=7/8
7/8+1/16=15/16
规律是加到最后的结果的分母就是最后一个数的分母，而分子比分母小1
所以原式=511/512

=511/512