Question

Ajutoor, dau coroana si puncte!! E urgent!! plss help

Answer 1

   
[tex]\displaystyle\\ \frac{2+5+8+\cdots+362}{3+7+11+\cdots+483}=?\\\\ \text{Si la numarator si la numitor avem cate o {\bf SUMA} de termeni in } \\ \text{progresie aritmetica pe care le vom calcula cu formula lui Gauss.}\\\\ \text{Pentru fiecare suma calculam numarul de termeni:}\\\\ \text{La numarator: }\\ n_1 = \frac{362-2}{3}+1=\frac{360}{3}+1=120+1={\bf121 \text{ de termeni}}\\\\ \text{La numitor: }\\ n_2 = \frac{483-3}{4}+1=\frac{480}{4}+1=120+1={\bf121 \text{ de termeni}} [/tex]


[tex]\displaystyle\\ \frac{2+5+8+\cdots+362}{3+7+11+\cdots+483}= \frac{\dfrac{121(362+2)}{2}}{ \dfrac{121(483+3)}{2}}=\frac{\dfrac{121\times364}{2}}{ \dfrac{121\times486}{2}}=\\\\ =\frac{121\times 182}{121\times 243}= \boxed{\bf \frac{182}{243}}[/tex]