Question

If a_n ≥ 1 for all n∈N (n ≥ 3), then the minimum value of log_a2 a₁ + log_a3 a₂ + log_a4 a₃ + ..... + log_a1 a_n is

(a) 0 

(b) 1 

(c) 2 

(d) None of these

Answer 1

(d) None of these

As an > 1 ∀ n ∈N, therefore 

log_a2 a₁ ≥ 0,  log_a3 a₂ ≥ 0,.......,log_a1 a_n ≥ 0

For positive numbers, AM > GM

The minimum value of the given sum is n, but as n > 3, n cannot take up the values 0, 1 or 2.