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

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

1/2+1/4+1/8+1/16+1/32+1/64+1/128
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/128
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/128
=1-1/128
=127/128
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1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32))+(1/32-1/64)+(1/64-1/128)
=1-1/128
=127/128