Question

1+2+2^2+2^3+....+2^2999 calculati ultima cifra

Answer 1

Uc(1+2+2^2+2^3+....+2^2999)=
=Uc(1)+Uc(2+2^2+2^3+....+2^2999)=
=Uc(1)+Uc(749*(2+4+8+16)+Uc(2^2997)+Uc(2^2998)+Uc(2^2999)=
=Uc(1)+Uc(20)+Uc(2^749*4+1)+Uc(2^749*4+2)+Uc(2^749+3)=
=Uc(1)+Uc(20)+Uc(2)+Uc(2^2)+Uc(2^3)=
=Uc(1+0+2+4+8)=Uc(15)=5

Answer 2

Se foloseste foirmula
1+2+2²+2³+.....2^2999 =(2^3000-1)/(2-1)=2^3000-1
atunci
U (2^3000) =U (2^4)=6
 U ( 2^3000-1) = U( U 2^3000)-U(1)) =U(6-1)=U(5)=5
Ultima cifra este 5