Make a proof about definition of limit.
I gather you are looking for the epsilon def'n of the limit...
For any ε > 0 you need to find an integer N > 0 so that if n > N then | 1 / n - 0 |< ε---> 1 / ε < n
...so choose N > 1/ε
Make a proof about definition of limit.
1/n, break the numerator and denominator into separate parts. As n—>infinity, the numerator remains unchanged. So we need only to worry about the denominator. The denominator approaches infinity. 1/∞ = 0.
You may also consider L'Hopital's rule. Take the derivative of the denominator, 1 (a constant) and the derivative is 0. Take the derivative of the denominator, n, and it becomes 1. The derivative of the numerator divided by the derivative of the denominator is 0.
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