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Determinati, va rog, ultima cifra a numarului 1+2+2^2 +2^3 +...+2^100

Răspuns :

S=1+2+2^2+2^3+....+2^100
2S=2+2^2+2^3+....+2^100+2^101
2S-S=2^101-1
S=2^101-1
U(2^101)=U[(2^4)^25x2^1]=U(16^25x2)=2
U(2-1)=1