1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/256
=1/2+1/4+1/8+1/16+1/32+1/32-1/256
=1/2+1/4+1/8+1/16+1/16-1/256
=1/2+1/4+1/8+1/8-1/256
=1/2+1/4+1/4-1/256
=1/2+1/2-1/256
=1-1/256
=255/256

等比数列，公比为1/2, 255/256 用公式Sn=a1(1-1/2^n)/(1-1/2)

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/256*256*【1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256】
=1/256*【128+64+32+16+8+4+2+1】
=1/256*255
=255/256能说明意思吗1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256...

全部展开

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/256*256*【1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256】
=1/256*【128+64+32+16+8+4+2+1】
=1/256*255
=255/256

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