Question

a=8+8^2+8^3+....+8^2012 este divizibil cu 10

Answer 1

[tex]A=8+8^2+8^3+...+8^{2012}\\ A=(8+8^2)+8^2(8+8^2)+...+8^{2010}(8+8^2) \\ A=(8+8^2)(1+8^2+...+8^{2010})\\ A=70(1+8^2+...+8^{2010})\\ A=7*10(1+8^2+...+8^{2010})[/tex]

Answer 2

8la 1 are ultima cifra=8
8la 2 are ultima cifra= 4
8la 3 ultima cifra=2
8la 4=6
8la 5=8

Ultima cifra se repeta din 4 in patru. 2012:4=503 si avem  503 repetari 8+4+2+6 = 20 iar numarul se termina in 0 care este divizibil cu 10