[tex]\displaystyle\\
f(x)=x+ \frac{1}{2} \\\\
f\left(- \frac{17}{2} \right)\cdot f\left(- \frac{15}{2} \right)\cdot ... \cdot f\left(\frac{21}{2} \right) = ?\\\\
\text{La numarator avem numere intregi impare consecutive}\\
\text{de la -17 pana la 21.}\\\\
\{-17;~-15;~-13;~-11;~-9;~-7;~-5;~-3;~-1;~1;~3;~5;\\\\
7;~9;~11;~13;~15;~17;~19;~21\}\\\\
f\left(- \frac{17}{2} \right)\cdot f\left(- \frac{15}{2} \right)\cdot ... \cdot f\left(- \frac{1}{2} \right)\cdot ... \cdot f\left(\frac{21}{2} \right) =
[/tex]
[tex]\displaystyle\\
=\left(-\frac{17}{2}+ \frac{1}{2} \right)\cdot \left(-\frac{15}{2}+ \frac{1}{2} \right)\cdot ... \cdot \underbrace{\left(-\frac{1}{2}+\frac{1}{2}\right)}_{=~0}\cdot ... \cdot \left(\frac{21}{2}+ \frac{1}{2} \right) =\\\\\\
=\left(-\frac{17}{2}+ \frac{1}{2} \right)\cdot \left(-\frac{15}{2}+ \frac{1}{2} \right)\cdot ... \cdot 0\cdot ... \cdot \left(\frac{21}{2}+ \frac{1}{2} \right) =0\\\\
\text{Observam ca unul din factori este egal cu zero.}
[/tex]
