1/3+1/6+1/12+1/24+……1/96简便计算

1/3+1/6+1/12+1/24+……1/96简便计算
1/3+1/6+1/12+1/24+……1/96简便计算
        

1/3+1/6+1/12+1/24+……1/96简便计算
=1/3*1 +1/3*2 +1/3*4+...+1/3*32
=1/3(1+1/2 +1/4 +1/8 + ...+1/32)
=1/3【1+(1-1/2) +(1/2-1/4)+（1/4-1/8）+（1/8-1/16）+（1/16-1/32)】
=1/3(1+1-1/32)
=2/3 -1/96
=63/96
=21/32
这个最简单了,你仔细看看,

1/3+1/6+1/12+1/24+……+1/96
=2/3-1/96
=21/32
1/3+1/6+1/12+1/24+……+1/96
=(1/3+1/6+1/12+1/24+……+1/96+1/96)-1/96
=(1/3+1/6+1/12+1/24+……+1/48)-1/96
=……
=(1/3+1/3)-1/96
=2/3-1/96
=64/96-1/96
=63/96
=21/32

2/3-1/96=63/96