1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
如果你是高中生,不知道等比数列的求和公式,那么可以这样做：
设S=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512①
则2S＝1＋1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256②
②－①,得
S＝1－1/512＝511/512

可以作图看出来，亦或是找规律511／512

令S=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
2S=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
S=2S-S=1-1/512=511/512

1/2=1-1/2
1/2+1/4=1-1/4
1/2+1/4+1/8=1-1/8
...
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512=1-1/512=511/512