1/2+1/4+1/8.+1/1024+1/2048

1/2+1/4+1/8.+1/1024+1/2048
1/2+1/4+1/8.+1/1024+1/2048

1/2+1/4+1/8.+1/1024+1/2048
1/2+1/4+1/8.+1/1024+1/2048
=1-1/2048
=2047/2048

2048是2的11次方，只是以1/2为首项，以1/2为等比的前11项等比数列的和，运用等比公式就可以
1/2+1/4+1/8......+1/1024+1/2048
=1/2*（1-(1/2）^11)/（1-1/2）
=1-1/2048
=2047/2048