■ラマヌジャンの連平方根(その6)

 (その5)をもう一度検算しておきたい.

√1+・・・=33/32=1+1/2^5

(1+1/8√1+・・・)=1+1/8+1/2^8=289/256

√(1+1/8√1+・・・)=17/16=1+1/2^4

(1+1/4√(1+1/8√1+・・・))=1+1/4+1/2^6=81/64

√(1+1/4√(1+1/8√1+・・・))=9/8=1+1/2^3

(1+1/2√(1+1/4√(1+1/8√1+・・・)))=1+1/2+1/2^4=25/24

√(1+1/2√(1+1/4√(1+1/8√1+・・・)))=5/4=1+1/2^2

(1+√(1+1/2√(1+1/4√(1+1/8√1−・・・))))=1+1+1/2^2=9/4

√(1+√(1+1/2√(1+1/4√(1+1/8√1−・・・))))=1+1/2=3/2

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