Chapter 1: 3P (page 17)

In the following problems, find the limit of the given sequence as
$n \to \infty$

Short Answer

Expert verified

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

As ${(- 1)}^{2 n} = 1$ 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.

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In the following problems, find the limit of the given sequence as
$n \to \infty$

Short Answer

Step by step solution

Definition of limits

Given parameters

Solve the limits

One App. One Place for Learning.

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In the following problems, find the limit of the given sequence asn→∞

Short Answer

Step by step solution

Definition of limits

Given parameters

Solve the limits

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

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Conservation of Energy and Momentum

Atoms and Radioactivity

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

In the following problems, find the limit of the given sequence as
$n \to \infty$