Question

Aflați suma tuturor numerele naturale format aaa.

Answer 1

111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 =
= 1 110×4 + 555 =
= 4 440 + 555 =
= 4 995
am grupat convenabil:
111+999 = 1 110
222+888 = 1 110
......

Answer 2

   
[tex]\displaystyle\\ \text{Numerele sunt:}\\ 111;222;333;444;555;666;777;888;999\\\\ \text{Suma lor este:}\\\\ S = 111+222;333+444+555+666+777+888+999= \\\\ = \frac{9(999+111)}{2}=\frac{9\times 1110}{2}=9\times 555 = \boxed{4995} [/tex]