1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496 一定要简便计算

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496 一定要简便计算
1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496 一定要简便计算

1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496 一定要简便计算
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

解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)×16/16+(1/31+1/62+1/124+1/248+1/496 ）×496/496
=（8+4+2+1）/16+(16+8+4+2+1）/496
=15/16+31/496
=15/16+1/16
=1

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