[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]
