Question

determinati ultima cifra a numarului
2⁰+2¹+2²+.......................+2²⁰¹³

Answer 1

e formula: 
2⁰+2¹+2²+.......................+2²⁰¹³ = 2^2014 - 1

4k    =6                        2014=4k+2 => U(2^2014)=4
4k+1=2                                                 U(2^2014-1)=3
4k+2=4
4k+3=8

Answer 2

[tex]1+2+(2^2+2^3+2^4+2^5)+(2^6+2^7+2^8+2^9) + ... \\\;\\ +(2^{2010} +2^{2011} +2^{2012} +2^{2013} ) =\\\;\\ 3+2(2+4+8+16)+2^5(2+4+8+16)+ ... +2^{2009}(2+4+8+16)=\\\;\\ 3+30(2+2^5+ ... +2^{2009}) =3+M_{10} \Longrightarrow u=3[/tex]