(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)

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(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
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(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)

(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
=(1+1∕2)(1-1/2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)/(1-1/2)
=(1-1∕2^2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)/(1-1/2)
=(1-1∕2^4)(1+1∕2^4)(1+1∕2^8)/(1-1/2)
=(1-1∕2^8)(1+1∕2^8)/(1-1/2)
=(1-1∕2^16)/(1-1/2)
=2-1/2^15

(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
=(1-1/2)(1+1∕2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)/(1-1/2)
=2(1-1/2^2)(1+1∕2^2)(1+1∕2^4)(1+1∕2^8)
=2(1-1∕2^4)1+1∕2^4)(1+1∕2^8)
=2(1-1∕2^8)(1+1∕2^8)
=2(1-1/2^16)
=2×65535/65536
=65535/32768