Question

demonstrati ca numarul a este divizibil cu 5 , unde : a = 2+4+6+...+78

Answer 1

   
[tex]\displaystyle \\ a = 2+4+6+...+78 \\ \\ \texttt{Calculam numarul de termeni: } \\ \\ n = \frac{78-2}{2} +1 = \frac{76}{2} +1 = 38 + 1 = 39 ~ \texttt{de termeni} \\ \\ S = \frac{39(78+2)}{2} = \frac{39\times 80}{2} = 39 \times 40 = \boxed{1560 } ~~ \text{si} ~~ \boxed{ 1560~ \vdots ~5 }\\ \\ \texttt{Numarul } 1560 \texttt{ este divizibil cu 5 deoarece ultima cifra}=0. [/tex]