The limit of the sequence \(\frac{(-1)^n}{n}\) as \(n\) approaches infinity is 0. This conclusion is derived from the fact that \((-1)^n\) alternates between 1 and -1, while \(\frac{1}{n}\) approaches 0. By applying the Squeeze Theorem, it is established that the oscillating behavior of the numerator does not affect the limit, as the denominator grows indefinitely. Therefore, the limit is definitively 0.
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Do you know the squeeze theorem?sara_87 said:Homework Statement
Find the limit as n tends to [itex]\infty[/itex] of:
[itex]\frac{(-1)^n}{n}[/itex]
Homework Equations
The Attempt at a Solution
I know that (-1)^n alternates between 1 and -1.
I also know that the limit of 1/n is 0. But I don't know how to compute the above limit.
Any ideas will be appreciated. Thank you.