■2乗保型数(その70)

[Q] √(x+1)−√x<εとなるxを求めよ.

  √(x+1)<√x+ε

  (x+1)<x+ε^2+2ε√x

  1−ε2<2ε√x

  x>{(1−ε2)/2ε}^2

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 (√2−1)^1=√2−√1

 (√2−1)^2=3−2√2=√9−√8

 (√2−1)^3=5√2−7=√50−√49

 (√2−1)^4=17−12√2=√289−√288

 (√2−1)^n=√(m+1)−√m

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