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1 Answer

S=1/2+1/4+1/8+...+1/8192.

S/2=1/4+1/8+1/16+...+1/8192+1/16384.

S-S/2=S/2=1/2-1/16384=8192/16384-1/16384=8191/16384.

So S=2×8191/16384=8191/8192.
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