What is limit of the sequence 1/n

Introduction : In the following question, we will find the limit of the sequence 1/n by using definition of the limit.

Question : Using definition of the limit to prove

\[limit_{n→∞}\frac{1}{n} =0\]

Solution :

definition of limit of a sequence

For all e>0 if there exists N∈ N such that

|a_n-L|<e for all n≥N

then

\[limit_{n→∞}x_n =L\]