Question

Calculati: (111 111+ 222 222+ 333 333+..........+999 999):(111+222+333+........+999)
[Suma lui Gauss]

Answer 1

(111 111+ 222 222+ 333 333+..........+999 999):(111+222+333+........+999)=
=1001(111+222+333+...+999):(111+222+333+........+999)=1001

Answer 2

111111(1+2+3+....+9)=111111(9x10):2=(111111x90):2=9999990:2=4.999.995

111(1+2+3+9)=111(10x9):2=(111x90_:2=9990:2=4.995

4999.995:4.995=1001