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Prove that lim(n->infinity) (1/n) = 0. Make a proof with definition of limit.

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2 Answers

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

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.

Comments

L'Hopitals Rule is used for indeterminate forms.
 
1/0 is considered undefined.

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