1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192

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1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192

1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192
1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192

1/128+1/256+1/512+1/1024+1/2048+1/4096+1/8192
= (1/128 - 1/8192 * 1/2)/(1-1/2)
= 127/8192