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

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