数学题1/2+1/4+1/8+1/16+1/32+1+641/2+1/4+1/8+1/16+1/32+1+64` 高手` 帮帮忙```还有 1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)

63/64 6/7
上面的每项可分解为(1-1/2)+(1/2-1/4)+...+(1/32-1/64)
下面的每项可分解为(1-1/2)+(1/2-1/3)+...+(1/6-1/7)

写错了吧,应该是
1/2+1/4+1/8+1/16+1/32+1/64
=1-1/64
=63/64
1/2+1/4+1/8+1/16+1/32+1+64
=1-1/32+65
=65 31/32
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

(1-1/2)+(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)+(1/2-1/3)+(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+1/64）-1/64
=1-1/64
=63/34

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

我有更简单的方法：1/2+1/4+1/8+1/16+1/32+1/64
=(1-1/2)+(1/2-1/4）+（1/4-1/8）+（1/8-1/16）+（1/16-1/32）+（1/32-1/64
1/2和1/2,1/4和1/4,1/8和1/8,1/16和1/16，1/32和1/32都对掉了，抵消了。就剩下 =1- 1/64
=63/64 这是最简单的方法！！！

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