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解：^表示乘方
原式=2×1/2×(1+1/2)(1+1/2²)(1+1/2^4)(1+2^8)+1/2^15
=2×(1-1/2)(1+1/2)(1+1/2²)(1+1/2^4)(1+2^8)+1/2^15
=2×(1-1/2²)(1+1/2²)(1+2^4)(1+1/2^8)+1/2^15
=2×(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15
=2×(1-1/2^8)(1+1/2^8)+1/2^15
=2×(1-1/2^16)+1/2^15
=2×1-2×1/2^16+1/2^15
=2-1/2^15+1/2^15
=2
原式=2×1/2×(1+1/2)(1+1/2²)(1+1/2^4)(1+2^8)+1/2^15
=2×(1-1/2)(1+1/2)(1+1/2²)(1+1/2^4)(1+2^8)+1/2^15
=2×(1-1/2²)(1+1/2²)(1+2^4)(1+1/2^8)+1/2^15
=2×(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15
=2×(1-1/2^8)(1+1/2^8)+1/2^15
=2×(1-1/2^16)+1/2^15
=2×1-2×1/2^16+1/2^15
=2-1/2^15+1/2^15
=2
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