that if an>=1 for all natural number n, then L >= 1.

My answer :

From the def of limit of sequence,

L-a(n) < epsilon and a(n) - L < epsilon

we know that a(n) >=1,

L - a(n) < epsilon => L must be larger than or same with a(n) to keep epsilon positive.

a(n) - L < epsilon => L must be larger than or same with a(n) to keep the equation on the left smaller than epsilon.

Is this argument acceptable?