Question

scrieti numarul an=111...1222...2 ca produs de doua cifre consecutive

Answer 1

a₁ = 12 = 3·4

a₂ = 1122 = 33·34

a₃ = 111222 = 333·334

a₄ = 11112222 = 3333·3334

.......

aₙ = 111...1222...2 = 333...3·33...34

333...3 = 999....9/3 = (1009...0 - 1)/4 =(10ⁿ-1)/3

$\Rightarrow a_n = \Big(\dfrac{10^n-1}{3}\Big)\cdot \Big(\dfrac{10^n-1}{3}+1\Big)$