What have you tried ?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.
SammyS said:What have you tried ?
What the heck !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.whattheheckV said:lim (1+n^2)^(e/eln(n))
n→∞
lim (1+n^2)^e
n→∞
A sequence is a list of numbers that follow a specific pattern or rule.
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.
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.
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.
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.