Question

In the following problems, find the limit of the given sequence as

$n\to \infty$

Short answer

The limit of the expressionis 0

Step-by-step solution

Definition of limits

A limit of a function/expression/sequence is used when the value of the function/sequence cannot be calculated directly or is difficult to calculate at a particular value. It is generally defined as the output obtained when the input is very close to the input value.

Given parameters

The given expression is

and the limit is $n\to \infty$

Solve the limits

Take $\frac{{\left(-1\right)}^n}{n}$inside the radical and simplify.

As ${\left(-1\right)}^{2n}=1$apply the limit $n\to \infty$ in the obtained expression.

Substitute 0 for $\frac{1}{n}$into the obtained expression and solve.

Thus, the limit of the given expression is 0.