Question

计算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^6)(1+1/2^8)+1/2^15

Answer 1

您好：

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^6)(1+1/2^8)+1/2^15

=2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^6)(1+1/2^8)+1/2^15

=2*(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^6)(1+1/2^8)+1/2^15

=...

=2*(1-1/2^16)+1/2^15

=2-1/2^15+1/2^15

=2

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