Question

determinati ultima cifra a numarului n,unde n=1+1+2+2 la puterea2+2 la puterea3+...+2 la putera 2004

Answer 1

[tex]n=1+2^1+2^2+....+2^{2004}\\ n=(1+2^1+2^2+2^3)+2^4(1+2+2^2+2^3)+...+2^{2001}(1+2+2^2+\\ 2^3)\\ n=(1+2+2^2+2^3)(1+2^4+...+2^{2001})\\ n=15(1+2^4+...+2^{2001})\\ Ultima\ cifra\ este\ 5.[/tex]