Question

Aratati ca 1+11+111+...+111111111=123456789

Answer 1

Ultimul numar are 9 cifre, deci logic ca cifra unitara se va repeta de 9 ori, cifra zecimala de 8 ori, cifra sutelor de 7...

Astfel obtii numarul 123456789

Answer 2

$1+11+111+...+111111111 = \\ \\ =111111111+11111111+1111111+...+111+11+1= \\ \\ = 12222222+1111111+...+1111+11+1 = \\ \\ = 123333333+111111+...+1111+11+1 = \\ \\ = 123444444+11111+1111+111+11+1 = \\ \\ = 123455555+1111+111+11+1 = \\ \\ = 123456666+111+11+1 = \\ \\ = 123456777+11+1 = \\ \\ = 123456788+1 = \\ \\ = 123456789$