Question

Va rog mult din suflet

Answer 1

   
[tex]\displaystyle\\ b)\\ \left(3- \frac{1}{3}\right)^{\b 2}+\left(2- \frac{1}{2}\right)^{\b 2}-\left(1\frac{1}{2}\right)^{\b 2}=\\\\ =\left(\frac{3\times3-1}{3}\right)^{\b 2}+\left(\frac{2\times2-1}{2}\right)^{\b 2}-\left(\frac{1\times2+1}{2}\right)^{\b 2}=\\\\ =\left(\frac{8}{3}\right)^{\b 2}+\underline{\left(\frac{3}{2}\right)^{\b 2}}-\underline{\left(\frac{3}{2}\right)^{\b 2}}=\left(\frac{8}{3}\right)^{\b 2}=\frac{64}{9}=\boxed{\bf 7\frac{1}{9}} [/tex]


[tex]\displaystyle\\ d)\\ \left(1-\frac{1}{2}\right)\times \left(1-\frac{1}{3}\right)\times \left(1-\frac{1}{4}\right)\times \cdots \times\left(1-\frac{1}{50}\right)=\\\\ =\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \cdots \times\frac{49}{50}= \boxed{\bf \frac{1}{50}}\\\\ \text{\bf Din oricare 2 fractii alaturate se simplifica numitorul fractiei}\\ \text{\bf din stanga cu numaratorul fractiei din dreapta.}[/tex]