Question

cine dorește sa ma ajute la ex 26 a)?

Answer 1

   
[tex]\displaystyle\\ 26)\\ a)\\ P_1 = \left(1- \frac{1}{2}\right)\cdot \left(1- \frac{1}{3} \right)\cdot \left(1- \frac{1}{4} \right)\cdot ... \cdot \left(1- \frac{1}{999} \right)\cdot\left(1- \frac{1}{1000} \right)=\\\\\\ = \left(\frac{1}{2}\right)\cdot \left(\frac{2}{3} \right)\cdot \left(\frac{3}{4} \right)\cdot ... \cdot \left(\frac{998}{999} \right)\cdot\left( \frac{999}{1000} \right)= [/tex]


[tex]\displaystyle\\ = \frac{1}{2}\cdot \frac{2}{3} \cdot \frac{3}{4} \cdot ... \cdot \frac{998}{999} \cdot \frac{999}{1000} = \boxed{\bf \frac{1}{1000}}\\\\ \texttt{Am simplificat, la fiecare 2 fractii alaturate, numitorul}\\ \texttt{fractiei din stanga cu numaratorul fractiei din dreapta.} [/tex]