Question

2^n+3+2^n+2+2^n+1+2^n/3^n+2+2*3^n+1+3^n​ este divizibil cu 6

Answer 1

Răspuns:

Explicație pas cu pas:

2^n+3+2^n+2+2^n+1+2^n = 2^n*(2^3 + 2^2 + 2^1 + 1) = 2^n*(8+ 4 + 2 + 1)

= 15*2^n = 5*3*2*2^n-1 = 5*6*2^n-1

3^n+2+2*3^n+1+3^n = 3^n*(3^2 + 2*3 + 1) = 3^n*(9 + 6 + 1) = 16*3^n

= 8*2*3*3^n-1 = 8*6*3^n-1

5*6*2^n-1 / 8*6*3^n-1 se simplifica  prin 6