Question

Determinați ultima cifra a numărului 2^0+2^1+2^2+2^3+....+2^2003

Answer 1

2^0=1
Uc(2^1+2^2+2^3+2^4)=Uc(2+4+8+16)=Uc(30)=0
2003:4=500 si rest 3
Uc(2^0+2^1+2^2+2^3+....+2^2003)=
=Uc(1+500×0+2^1+2^2+2^3)=
=Uc(1+0+2+4+8)=Uc(15)=5

Answer 2

numarul este (2^2004-1)/(2-1)=2^2004-1

U(2^2004)=U(2^4)=U(16)=6

U(6-1)=U(5)=5