Find the limit of the given sequence

[whattheheckV]

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]

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 ?

 

[whattheheckV]

What have you tried ?

lim (1+n^2)^(e/eln(n))
n→∞

lim (1+n^2)^e
n→∞

 

[SammyS]

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

 

[Mark44]

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.