Chapter 1: 4P (page 17)

In the following problems, find the limit of the given sequence as $n \to \infty$
$\frac{{(2)}^{n}}{n^{2}}$

Short Answer

Expert verified

The limit of the expression $\frac{{(2)}^{n}}{n^{2}}$ is $\infty$

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 $\frac{2^{n}}{n^{2}}$ and the limit $n \to \infty$

Solve the limits

Take the limit asin the obtained expression and apply the L'Hôpital's rule on the expression inside the limit.

Again, apply the L'Hôpital's rule in the obtained expression.

As the limit of the exponential function when is , thus the limit of the given expression is $\infty$

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In the following problems, find the limit of the given sequence as $n \to \infty$
$\frac{{(2)}^{n}}{n^{2}}$

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→∞2nn2

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

Oscillations

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Study anywhere. Anytime. Across all devices.

In the following problems, find the limit of the given sequence as $n \to \infty$
$\frac{{(2)}^{n}}{n^{2}}$