Question

aflati ultima cifra a nr 2 la puterea 1 + 2 la puterea 2 ....... + 2 la puterea a 2012

Answer 1

S= 2^1 +2^2 + ... + 2^2012 2S= 2^2 + 2^3 + ... + 2^2013 2S - S= (2^2 + 2^3 + ... + 2^2013) - (2^1 + 2^2 +... + 2^2012) S= 2^2013 - 2^1 (asta ramane dupa scadere) S= 2^2013 - 1 U(ultima cifra) 2^x = 2, 4, 8, 6 (se repeta din 4 in 4) 2013:4=503 rest 1 => U (x^2013 =1) => U (2^2013 -1) =1-1 =0 Raspuns: 0.