数学题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.

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

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

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