(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/32 +1) 简便算法

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/18 12:02:30
(2^-1/2+1)(2^-1/4+1)(2^-1/8+1)(2^-1/16+1)(2^-1/32+1)简便算法(2^-1/2+1)(2^-1/4+1)(2^-1/8+1)(2^-1/16+1)(2^

(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/32 +1) 简便算法
(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/32 +1) 简便算法

(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/32 +1) 简便算法
(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/32 +1)(2^-1/32 -1)/(2^-1/32 -1)
=(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/16 +1)(2^-1/16-1)/(2^-1/2 -1)
=(2^-1/2 +1)(2^-1/4 +1)(2^-1/8 +1)(2^-1/8-1)/(2^-1/2 -1)
=(2^-1/2 +1)(2^-1/4 +1)(2^-1/4-1)/(2^-1/2 -1)
=(2^-1/2 +1)(2^-1/2-1)/(2^-1/2 -1)
=(2^-1-1)/(2^-1/2 -1)
=-1/2/(√2/2-1)
=1/(2-√2)
=(2+√2)/2