Réponse :
Bonjour,
Explications étape par étape :
[tex]\dfrac{3}{4} =\dfrac{1}{2}+\dfrac{1}{4}\\\\\dfrac{18}{7}=2+\dfrac{1}{2}+\dfrac{1}{14}\\\\\dfrac{17}{11}=1+\dfrac{1}{2}+\dfrac{1}{22}\\\\\dfrac{2001}{2002}=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{43}+\dfrac{1}{18447}[/tex]
Explications:
[tex]\boxed{\dfrac{3}{4}}\\\\\dfrac{4}{3}=1.333.... = > 2\ (on\ prend\ le\ naturel \ sup\' erieur)\\\\\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{3-2}{4}=\dfrac{1}{4}\ (fin)\\[/tex]
[tex]\boxed{\dfrac{2001}{2002}}\\\\\dfrac{2002}{2001}=1,000499... = > 2\\\\\dfrac{2001}{2002}-\dfrac{1}{2}=\dfrac{2000}{4004}\\\\\dfrac{4004}{2000}=2,002 == > 3\\\\\dfrac{2000}{4004}-\dfrac{1}{3}=\dfrac{1996}{12012}\\\\\dfrac{12012}{1996}=6.0180... = > 7\\\\\dfrac{1996}{12012}-\dfrac{1}{7}=\dfrac{1960}{84084}\\\\\dfrac{84084}{1960}=42.9 = > 43\\\\...\\[/tex]
