Question

Ultima cifra a produsului 2001x2002x2003x2004x...x2009

Answer 1

2001×2002×2003×2004×...×2009 = 523 631 966 829 050 994 132 853 514 880

Deci ultima cifra este 0, dar trebuie sa o aflam prin calcule.

U(2001×2002×2003×2004×...×2009) = U(1×2×3×4...×9) = 

Caracterele ingrosate arata ce voi calcula in continuare.

= U(1)×U(2)×U(3) ×U(4)×...×U(9) = U(6) × U(4)×U(5)×U(6)×U(7)×U(8)×U(9) =
 = U(6) × 0 × U(6)×U(7)×U(8)×U(9) =  [ U(6) × U(6)×U(7)×U(8)×U(9) ] × 0 = 0


=>  U(2001×2002×2003×2004×...×2009) = 0