1/2+1/4+1/8+1/16+1/32+1/64=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=

1/2+1/4+1/8+1/16+1/32+1/64=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=
1/2+1/4+1/8+1/16+1/32+1/64=
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=

1/2+1/4+1/8+1/16+1/32+1/64=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=
1/2+1/4+1/8+1/16+1/32+1/64
=1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64
=1-1/64
=63/64
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

1/2+1/4+1/8+1/16+1/32+1/64
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/32-1/64)
=1-1/64
=63/64
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7=
=(1-1/2)+(1/2-1/3)+...+(1/6-1/7)
=1-1/7
=6/7

第一个式子是等比数列。由公式可得
Sn=A1(1-q^n)/(1-q)或Sn=(a1-an*q)/(1-q)（q≠1）
可得S和=1/2（1-（1/2)^6）/(1-1/2) 可知q=1/2
S=63/64
第二式可化为：
（1-1/2）+（1/2-1/3）+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
这样可得：S=1-1/7=6/7