Question

Stabiliți dacă are loc egalitatea: (vedeți în poză)​

Answer 1

$\displaystyle 1+\frac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1} } } } } = 1+\frac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+1 } } } } = 1+\frac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{2} } } } =\\\\\\=1+\frac{1}{1+\cfrac{1}{1+\cfrac{1}{\cfrac{2+1}{2} } } } =1+\frac{1}{1+\cfrac{1}{1+\cfrac{1}{\cfrac{3}{2} } } } =1+\frac{1}{1+\cfrac{1}{1+ 1 \cdot \cfrac{2}{3} }}=$

$\displaystyle =1+\frac{1}{1+\cfrac{1}{1+\cfrac{2}{3} } } =1+\frac{1}{1+\cfrac{1}{\cfrac{3+2}{3} } } =1+\frac{1}{1+\cfrac{1}{\cfrac{5}{3} } } =1+\frac{1}{1+1 \cdot \cfrac{3}{5} } =\\\\=1+\frac{1}{1+\cfrac{3}{5} } =1+\frac{1}{\cfrac{5+3}{5} } =1+\frac{1}{\cfrac{8}{5} } =1+1 \cdot \frac{5}{8} =1+\frac{5}{8} =\frac{8+5}{8}=\boxed{ \frac{13}{8} }$