1/2+1/4+1/6+1/8+1/16+1/32=

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1/2+1/4+1/6+1/8+1/16+1/32=
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1/2+1/4+1/6+1/8+1/16+1/32=
1/2+1/4+1/6+1/8+1/16+1/32=

1/2+1/4+1/6+1/8+1/16+1/32=
1/2+1/4+1/6+1/8+1/16+1/32
=1/2+1/4+1/8+1/16+1/32+1/32-1/32
=1/2+1/4+1/8+1/16+1/16-1/32
=1/2+1/4+1/8+1/8-1/32
=1/2+1/4+1/4-1/32
=1/2+1/2-1/32
=1-1/32
=31/32

先把所有的分母都转换成以32为底，再进行相加

S=1/2+1/4+1/6+1/8+1/16+1/32..........(1)
2S=1+1/2+1/4+1/6+1/8+1/16.............(2)
(2)-(1)
S=1/2+1/4+1/6+1/8+1/16+1/32=1-1/32=31/32

1/2+1/4+1/6+1/8+1/16+1/32
=1-1/2+1/2-1/4+1/6+1/4-1/8+1/8-1/16+1/16-1/32
=1+1/6-1/32
=109/96