■電卓と2乗保型数(その72)
[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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