The discussion revolves around finding the limit of the sequence (1+n^2)^(1/ln(n)) as n approaches infinity. Participants are exploring the behavior of this expression and its limit.
The discussion is ongoing, with participants raising questions about the steps taken in their reasoning and exploring different interpretations of the limit. Some guidance has been offered regarding the logarithmic approach, but no consensus has been reached.
There is a mention of a reference to Wolfram's output, which suggests a specific limit, but participants express confusion about the reasoning behind it. The discussion includes considerations of how to handle the exponents in the limit expression.
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→∞