1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496（简单一点）

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496（简单一点）
1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496（简单一点）

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496（简单一点）
没打错?觉得应该是32 64 128 256 512

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496
=(1/2+1/4+1/8+1/16+1/16+1/31+1/62+1/124+1/248+1/496+1/496)-1/496-1/16
=(1/2+1/4+1/8+1/8+1/31+1/62+1/124+1/248+1/248)-1/496-1/16
=(1/2+1/4+1/4+1...

全部展开

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496
=(1/2+1/4+1/8+1/16+1/16+1/31+1/62+1/124+1/248+1/496+1/496)-1/496-1/16
=(1/2+1/4+1/8+1/8+1/31+1/62+1/124+1/248+1/248)-1/496-1/16
=(1/2+1/4+1/4+1/31+1/62+1/124+1/124)-1/496-1/16
=(1/2+1/2+1/31+1/62+1/62)-1/496-1/16
=(1+1/31+1/31)-1/496-1/16
=1+2/31-1/496-1/16
=1+(32-1-31)/496
=1

收起

1/2+1/4+1/8+1/16=15/16 1/31+1/62+1/124+1/248+1/496=31/496=1/16
15/16+1/16=1
1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496=1