# Find the limit of the given sequence

• whattheheckV
In summary, the given limit is (1+n^2)^(1/ln(n)) and Wolfram's answer is e^2, but the reasoning behind this answer is unclear. Further help is needed to understand the solution.
whattheheckV
OP has been warned about posting a problem with no apparent effort

## Homework Statement

Find the limit of the given sequence as n →∞

## Homework Equations

(1+n^2)^(1/ln(n))

## The Attempt at a Solution

Wolfram said the answer was e^2, though i cannot figure out why. Any help would be greatly appreciated.

whattheheckV said:

## Homework Statement

Find the limit of the given sequence as n →∞

## Homework Equations

(1+n^2)^(1/ln(n))

## The Attempt at a Solution

Wolfram said the answer was e^2, though i cannot figure out why. Any help would be greatly appreciated.
What have you tried ?

SammyS said:
What have you tried ?

lim (1+n^2)^(e/eln(n))
n→∞

lim (1+n^2)^e
n→∞

whattheheckV said:
lim (1+n^2)^(e/eln(n))
n→∞

lim (1+n^2)^e
n→∞
What the heck !

How about e^(ln( the limit ))

ln of the limit is limit of ln .

What is ##\displaystyle\ \ln\left( (1+n^2)^{1/\ln(n)}\right) \ ?##

whattheheckV said:
lim (1+n^2)^(e/eln(n))
n→∞

lim (1+n^2)^e
n→∞
Is the outer exponent above ##\frac e {eln(n)}##? If so, how did you go from and exponent of ##\frac e {eln(n)}## to an exponent of e? If you "cancel" the factors of e you would be left with an exponent of ##\frac 1 {ln(n)}##, which gets you right back to where you started.

## 1. What is a sequence?

A sequence is a list of numbers that follow a specific pattern or rule.

## 2. How do you find the limit of a sequence?

To find the limit of a sequence, you need to determine what value the sequence approaches as the number of terms increases. This can be done by analyzing the behavior of the terms in the sequence and using mathematical techniques such as algebraic manipulation, graphing, or the comparison test.

## 3. What is the importance of finding the limit of a sequence?

Finding the limit of a sequence is important because it helps us understand the behavior of the sequence and determine if it converges or diverges. This information is useful in a variety of fields, including physics, economics, and computer science.

## 4. Can a sequence have more than one limit?

No, a sequence can only have one limit. If a sequence has more than one limit, it is considered divergent and does not have a well-defined limit.

## 5. Are there any special cases when finding the limit of a sequence?

Yes, there are some special cases when finding the limit of a sequence, such as when the sequence is oscillating between two values or when the terms in the sequence alternate in sign. In these cases, additional techniques, such as the squeeze theorem or the alternating series test, may be used to find the limit.

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