# Homework Help: Find the limit of the given sequence

1. May 14, 2015

### whattheheckV

• OP has been warned about posting a problem with no apparent effort
1. The problem statement, all variables and given/known data
Find the limit of the given sequence as n →∞

2. Relevant equations
(1+n^2)^(1/ln(n))

3. The attempt at a solution
Wolfram said the answer was e^2, though i cannot figure out why. Any help would be greatly appreciated.

2. May 14, 2015

### SammyS

Staff Emeritus
What have you tried ?

3. May 14, 2015

### whattheheckV

lim (1+n^2)^(e/eln(n))
n→∞

lim (1+n^2)^e
n→∞

4. May 14, 2015

### SammyS

Staff Emeritus
What the heck !

How about e^(ln( the limit ))

ln of the limit is limit of ln .

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

5. May 14, 2015

### Staff: Mentor

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.