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问题: 计算

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16=

解答:

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