Question

determinati ultima cifra a numarului n unde n=1+1+2+2^2+2^3+...+2^2004

Answer 1

n = 1 + 1 + 2 + 2^2 + 2^3 +... + 2^2004

Fie p = 1 + 2 + 2^2 + 2^3 +...+ 2^2003+2^2004

p = 2^0 + 2^1 + 2^2 + ...+ 2^2003 + 2^2004 |×2

2×p = 2^1 + 2^2 +2^3 +...+ 2^2004 + 2^2005

2×p - p = 2^2005 - 2^0

p = 2^2005 - 1
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n = 1 + p

n = 1 + 2^2005 - 1

n = 2^2005

U(2^2005) = U(2^4×501+1) = U(2^1) = 2

asadar,

U(n) = 2
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