1/2+1/4+1/8……+1/256+1/512+1/1024 简便计算,

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1/2+1/4+1/8……+1/256+1/512+1/1024简便计算,1/2+1/4+1/8……+1/256+1/512+1/1024简便计算,1/2+1/4+1/8……+1/256+1/512+

1/2+1/4+1/8……+1/256+1/512+1/1024 简便计算,
1/2+1/4+1/8……+1/256+1/512+1/1024 简便计算,

1/2+1/4+1/8……+1/256+1/512+1/1024 简便计算,
=1/2+1/4+1/8……+1/256+1/512+1/1024 +1/1024-1/1024
=1/2+1/4+1/8……+1/256+1/512+1/512-1/1024
=1-1/1024
=1023/1024

　Sn =(a1-an*q)/(1-q) (q≠1) ={1/2-1/1024*(1/2)}/(1-1/2)=(1/2-1/2048)/(1/2)=1023/1024