作业帮 > 数学 > 作业

(1+1/2)(1+1/2的平方)(1+1/2的四次方)(1+1/2的八次方)(1+1/2的十六次方)+(1+2的31次

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/03 11:32:53
(1+1/2)(1+1/2的平方)(1+1/2的四次方)(1+1/2的八次方)(1+1/2的十六次方)+(1+2的31次方)
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+(1+2^31)=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2²)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^16)(1+1/2^16)×2+ 1+1/2^31
=2-1/2^31+1+1/2^31
=3