Questions mathématiques diverses

Question 56:

X=11+11+1+11+1+1+11+1+1+1+11+1+1+1+1+11+1+1+1+1+1+11+1+1+1+1+11+1+1+1+11+1+1+11+1+11+11=?X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{1+1}}{1+1+1}}{1+1+1+1}}{1+1+1+1+1}}{1+1+1+1+1+1}}{1+1+1+1+1+1+1}}{\dfrac{1+1+1+1+1+1}{\dfrac{1+1+1+1+1}{\dfrac{1+1+1+1}{\dfrac{1+1+1}{\dfrac{1+1}{1}}}}}}=?
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$X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{1+1}}{1+1+1}}{1+1+1+1}}{1+1+1+1+1}}{1+1+1+1+1+1}}{1+1+1+1+1+1+1}}{\dfrac{1+1+1+1+1+1}{\dfrac{1+1+1+1+1}{\dfrac{1+1+1+1}{\dfrac{1+1+1}{\dfrac{1+1}{1}}}}}}=?$
Réponse 56:
X=1234567654321X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{2}}{3}}{4}}{5}}{6}}{7}}{\dfrac{6}{\dfrac{5}{\dfrac{4}{\dfrac{3}{\dfrac{2}{1}}}}}} =16456765432=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{6}}{4}}{5}}{6}}{7}}{\dfrac{6}{\dfrac{5}{\dfrac{4}{\dfrac{3}{2}}}}} =1245676583=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{24}}{5}}{6}}{7}}{\dfrac{6}{\dfrac{5}{\dfrac{8}{3}}}} =172076158=\dfrac{\dfrac{\dfrac{1}{720}}{7}}{\dfrac{6}{\dfrac{15}{8}}} =150404815=\dfrac{\dfrac{1}{5040}}{\dfrac{48}{15}} =116128=\dfrac{1}{16128}

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