Question

aflati ultima cifra a numarului n unde n=1+1+2+2^2+2^3+...+2^2018

Answer 1

    
[tex]\text{Folosim formula:} \\ 1+2+2^2+2^3+...+2^{2018} = \\ \\ =2^0+2^1+2^2+2^3+...+2^{2018} =2^{2018 + 1} - 1 =\boxed{2^{2019} - 1 }\\ ---- \\ \Longrightarrow~~n=1+1+2+2^2+2^3+...+2^{2018}=2^{2019} - 1 + 1 = \boxed{2^{2019}} \\ \\ \text{Calculam ultima cifra a numarului: }~2^{2019} \\ \\ U(2^{2019}) = U(2^{2016+3})=U(2^{2016} \times 2^3)=U(2^{4 \times 504} \times 2^3)= \\ \\ =U\Big(\Big(2^{4}\Big)^{504} \times 2^3 \Big)=U\Big(16^{504} \times 2^3 \Big)=U(6 \times 8) = U(48) = \boxed{8}[/tex]