To evaluate the limit of a sequence $ \{a_n\}$, we use the tactic of evaluating the expression $ \lim_{n \to \infty}a_n $. Also, at times, when we have a guess of the limit (say $l$) of a sequence, we can try to prove that $l$ is the limit of that sequence, using the definition of limit.
However, I would like to know a method of finding the limit of the sequence using definition. That is, my question is :
Evaluate the limit of the sequence $\left(\frac 1 n\right)$ using the definition of limit.
and not:
Prove that $0$ is the limit of the sequence $\left(\frac 1 n\right)$ using the definition of limit.
Is there any procedure to do this? Other than guessing the limit and then proving it.