Question

vă rog cine poate sa ma ajute?

Answer 1

ATAT POT FACE!
Imi pare rau!

Answer 2

   
[tex]\displaystyle\\ A= \frac{7}{4\cdot 3} +\frac{8}{5\cdot 3} +\frac{9}{6\cdot 3} + \cdots + \frac{20}{17\cdot 3}\\\\ B = \frac{1}{3\cdot 4}+\frac{2}{3\cdot 5}+\frac{3}{3\cdot 6}+\cdots +\frac{14}{3\cdot 17}\\\\ \text{Observam ca fiecare sir are 14 termeni.}\\ \text{Descompunem fiecare fractie de la A si de la B.} [/tex]


[tex]\displaystyle\\ A = \underbrace{\frac{1}{4}+ \frac{1}{3}}+\underbrace{\frac{1}{5}+ \frac{1}{3}}+\underbrace{\frac{1}{6}+ \frac{1}{3}}+ \cdots + \underbrace{\frac{1}{17}+ \frac{1}{3}}=\\\\ = \Big(\underbrace{\frac{1}{3}+ \frac{1}{3}+ \frac{1}{3}+\cdots+ \frac{1}{3}}_{\texttt{De 14 ori}}\Big) +\Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)=\\\\ =\boxed{\frac{14}{3} + \Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)}[/tex]


[tex]\displaystyle\\ B = \underbrace{\frac{1}{3} -\frac{1}{4}}+\underbrace{\frac{1}{3} -\frac{1}{5}}+ \underbrace{\frac{1}{3} -\frac{1}{6}}+\cdots + \underbrace{\frac{1}{3} -\frac{1}{17}}=\\\\ =\Big(\underbrace{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\cdots+\frac{1}{3}}_{\texttt{De 14 ori}}\Big) - \Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)=\\\\\\ = \boxed{\frac{14}{3} - \Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)}[/tex]


[tex]\displaystyle\\ A+B = \\\\ \frac{14}{3} + \underline{\Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)}+ \frac{14}{3} - \underline{\Big(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots+\frac{1}{17}\Big)}=\\\\ =\frac{14}{3}+\frac{14}{3} =\boxed{\bf\boxed{\bf \frac{28}{3}}}[/tex]