Question

aflati ultima cifra a nr 7+7^2+7^3+.........+7^43

Answer 1

[tex]S=7+7^{2}+7^{3}+....+7^{43}|*7\\7S=7*(7+7^{2}+7^{3}+...+7^{43}\\ 7S=7*7+7*7^{2}+7*7^{3}+...+7*7^{43}\\7S=7^{1+1}+7^{2+1}+7^{3+1}+...+7^{43+1} \\7S=7^{2}+7^{3}+7^{4}+....+7^{44}\\7S=(7+7^{2}+7^{3}+...+7^{43})+7^{44}-7 \\7S=S+7^{44}-7\\7S-S=7^{44}-7\\6S=7^{44}-7\\S=\frac{7^{44}-7}{6}\\ U(7^{44})=U(7^{4*11})=U(7^{4})=U(2401)\\U(\frac{2401-7}{6})=U(\frac{2394}{6})=U(399)=9[/tex]