studiem fiecare paranteza
[tex]\frac{1}{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}{99} = \frac{99}{99} + \frac{1}{99} = \frac{100}{99}[/tex]
adunare si scaderea fractiilor se face doar daca au numitor comun
[tex]\frac{x}{y} : \frac{a}{b} = \frac{x}{y} * \frac{b}{a}[/tex]
transformam impartirea in inmultire
[tex]\frac{1}{1} * \frac{2}{3} * \frac{3}{4} * ... * \frac{99}{100} =[/tex]
facem simplificari si ramanem doar cu
[tex]= \frac{1}{1} * \frac{2}{1} * \frac{1}{100} = \frac{2}{100} = \frac{1}{50}[/tex]
