如题所述
二分之一加四分之三加八分之七加八分之七加十六分之十五........加一千零二十四分之一千零二十三
=1/2+3/4+7/8+15/16+...+1023/1024
=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+...+(1-1/1024) ∵[2^10=1024]，∴有10项。
=10-(1/2+1/4+1/8+1/16+...+1/1024)
=10-[(2^9/2^10)+(2^8/2^10)+(2^7/2^10)+...+(2^0/2^10)]
=10-(2^9+2^8+2^7+...+2^0)/1024
=10-(512+256+128+64+32+16+8+4+2+1)/1024
=10-1023/1024
=9又1/1024
=1/2+3/4+7/8+15/16+...+1023/1024
=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+...+(1-1/1024) ∵[2^10=1024]，∴有10项。
=10-(1/2+1/4+1/8+1/16+...+1/1024)
=10-[(2^9/2^10)+(2^8/2^10)+(2^7/2^10)+...+(2^0/2^10)]
=10-(2^9+2^8+2^7+...+2^0)/1024
=10-(512+256+128+64+32+16+8+4+2+1)/1024
=10-1023/1024
=9又1/1024
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