1/2+1/4+1/8+1/16+1/32+1/64=

1/2+1/4+1/8+1/16+1/32+1/64=
1/2+1/4+1/8+1/16+1/32+1/64=

1/2+1/4+1/8+1/16+1/32+1/64=
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.
是否可以解决您的问题?

由1/2+1/4可以得到3/4 由1/2+1/4+1/8可以得到7/8 以此类推，原式就可以等于63/64

=1-64分之1
=64分之63
（咳咳还有不懂问啊，偶六年级赚分不容易记得点采纳回答！）

分母全化64，得61/64

先通分，分公分母是64，既有32/64+16/64+8/64+4/64+2/64+1/64=63/64

记S= 1/2+1/4+1/8+1/16+1/32+1/64,
那么2S = 1+1/2+1/4+1/8+1/16+1/32,
然后 2S-S =S= 1-1/64 = 63/64