1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512=多少

令T=1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512
则2T=1+1/2+1/4+1/8+1/16+1/64+1/128+1/256
T=2T-T
=(1+1/2+1/4+1/8+1/16+1/64+1/128+1/256)-(1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512)
=1+1/2+1/4+1/8+1/16+1/64+1/128+1/256-1/2-1/4-1/8-1/16-1/64-1/128-1/256-1/512
=1-1/512
=511/512

用裂项法解，1/2 = 1 - 1/2， 1/4 = 1/2 - 1/4， 1/8 = 1/4 - 1/8，原式就等于
1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 ... + 1/512 - 1/1024
所以=1 - 1/1024 = 1023/1024不知道你是不是少写了一个1/32，如果没有，恢复，在给你另外的答案

先找规律：
1/2+1/4=3/4
1/2+1/4+1/8=7/8
1/2+1/4+1/8+1/16=15/16
……
所以原式=511/512