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

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 14:53:48

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

化简(1+1/2^2)(1+1/2^4 )(1+2/2^8)(1+2/2^16)
(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)
=(1-1/2^2)(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注:即上下同乘(1-1/2^2)
=(1-1/2^4)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注:平方差公式
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2^2)
=(1-1/2^16)(1+1/2^16)/(1-1/2^2)
=(1-1/2^32)/(1-1/2^2)
=(1-1/2^32)/(3/4)
=(4-1/2^30)/3