题目

计算:(1+½)(1+1/2²)(1+2的四次方分之一)(1+2的十六次方分之一)
要巧算

提问时间：2020-08-02

答案

(1+½)(1+1/2²)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2)(1+½)(1+1/2²)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2²)(1+1/2²)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2^8)(1+1/2^8)(1+1/2^16)
=2(1-1/2^16)(1+1/2^16)
=2(1-1/2^32)
=2 -1/2^31
^表示指数,2^31表示2的31次方.