Question

1+3+3^2+3^3+........3^100=?Va rog!!Dau coroana+12 puncte!!!

Answer 1

1+3+3^2+3^3+........3^100=1+3^(1+2+3+...+100)
=1+3^(100•101:2)
=1+3^(10100:2)
=1+3^5050
=1+[ U(3^5050)]
U(3^1)=3
U(3^2)=9
U(3^3)=7
U(3^4)=1
U(3^5)=3
Constatăm că avem 4 variante pentru ultima cifra a lui 3 la o putere.
=1+{U[3^(5050:4)]}
=1+[U(3^4•1262+2)]
=1+[ U(3^2)]
=1+9
=10