impartirea a doua fractii
[tex]\frac{a}{b} : \frac{c}{d} = \frac{a}{b} *\frac{d}{c}[/tex]
studiem fiecare paranteza
[tex]1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}[/tex]
[tex]1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}[/tex]
[tex]1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}[/tex]
[tex]1 + \frac{1}{99} = \frac{99}{99} + \frac{1}{99} = \frac{100}{99}[/tex]
avem 98 de paranteze , de la 1/2 la 1/99, si 1 la inceput
[tex]1 :\frac{3}{2} : \frac{4}{3} : \frac{5}{4} : ... : \frac{100}{99} =[/tex]
[tex]=1 * \frac{2}{3} * \frac{3}{4} * \frac{4}{5} * ... * \frac{99}{100} =[/tex]
simplificam si obtinem
[tex]= 1 * \frac{2}{1} * \frac{1}{100} =[/tex][tex]\frac{2}{100}[/tex]
[tex]= \frac{1}{50}[/tex]
