简算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^15)题错了,改正下:(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 06:12:09
简算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^15)题错了,改正下:(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

简算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^15)题错了,改正下:(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
简算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^15)
题错了,改正下:(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15

简算(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^15)题错了,改正下:(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=[(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15]×(1-1/2)/(1-1/2)
=[(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+(1-1/2)×1/2^15]/(1-1/2)
=[(1-1/2²)(1+1/2^2)(1+1/2^4)(1+1/2^8)+(1-1/2)×1/2^15]/(1/2)
=[(1-1/2⁴)(1+1/2^4)(1+1/2^8)+(1-1/2)×1/2^15]/(1/2)
=(1-1/2^8)(1+1/2^8)+(1-1/2)×1/2^15]/(1/2)
=(1-1/2^16+1/2^15-1/2^16)/(1/2)
=(1-1/2^16×2+1/2^15)/(1/2)
=(1-1/2^15+1/2^15)/(1/2)
=1/(1/2)
=2
不懂还可问,o(∩_∩)o