计算1/3+1/6+1/12+1/24+……+1/384的过程和答案

解法一：

1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384

＝1/3+1/6+1/12+1/24+1/48+1/96+1/192＋1/192－1/384

＝1/3+1/6+1/12+1/24+1/48+1/96＋1/96－1/384

＝1/3+1/6+1/12+1/24+1/48＋1/48－1/384

＝1/3+1/6+1/12+1/24＋1/24－1/384

＝1/3+1/6+1/12+1/12－1/384

＝1/3+1/6+1/6－1/384

＝1/3+1/3－1/384

＝2/3－1/384

＝255/384

＝85/128

解法二：

1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384

=1/3(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128)

=1/3(1-1/256)×2

=85/128

解法三：

1/3+1/6+1/12+1/24+1/48+1/96+1/192+1/384

=（384÷3+384÷6+384÷12+384÷24+384÷48+384÷96+384÷192+384÷384）/384

=（128+64+32+16+8+4+2+1）/384

=255/384

=85/128