Question

5 supra 6 <1 supra 101 +1 supra 101+1 supra 102+...+1 suora 600<5

Answer 1

Răspuns

Explicație pas cu pas:

$\dfrac{1}{600} < \dfrac{1}{101} < \dfrac{1}{100}\\\\\dfrac{1}{600} <\dfrac{1}{102} <\dfrac{1}{100}\\\\\dfrac{1}{600} < \dfrac{1}{103} < \dfrac{1}{100}\\ ~~~~~~~~~~~~\vdots\\\\\dfrac{1}{600} \leq \dfrac{1}{600} < \dfrac{1}{100}\\\\\underbrace{\dfrac{1}{600}+\dfrac{1}{600}+\ldots +\dfrac{1}{600}}<\dfrac{1}{101}+\dfrac{1}{102}+\ldots+\dfrac{1}{600}< \underbrace{\dfrac{1}{100}+\dfrac{1}{100}+\ldots+\dfrac{1}{100}}\\~~~~~~~~~~de~500~ori~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~de~500~ori$

$\dfrac{500}{600}<\dfrac{1}{101}+\dfrac{1}{102}+\ldots+\dfrac{1}{600}<\dfrac{500}{100}\\\\\dfrac{5}{6}<\dfrac{1}{101}+\dfrac{1}{102}+\ldots+\dfrac{1}{600} <5, Q.E.D.$