1/2(1+1/2)(1+1/4)(1+1/16)(1+1/256)
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1/2(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=(1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=(1-1/4)((1+1/4)(1+1/16)(1+1/256)
=(1-1/16)(1+1/16)(1+1/256)
=(1+1/256)(1+1/256)
=1-1/65536
=65535/65536
