# Math Help - urgent assignment question limit

1. ## urgent assignment question limit

lim [ ((1+5/n)^n) / e^5 ] ^n hint: use lny

2. Originally Posted by david-david
lim [ ((1+5/n)^n) / e^5 ] ^n hint: use lny
Im assuming n is going to infinity. And I think you have a typo. As it is we have

$\lim_{n\to\infty}\left(\frac{\left(1+\frac{5}{n}\r ight)^n}{e^5}\right)^n$

Is that correct?

3. yes thats correct, can u solve it please

4. Taking into consideration that we have:

$\color{blue}\boxed{\lim_{n \to \infty} \left(1+\frac {a}{n}\right)^{bn} = e^{ab}}$

so we have:

$\lim_{n\to\infty}\left(\frac{\left(1+\frac{5}{n}\r ight)^n}{e^5}\right)^n=\lim_{n\to\infty}\left(\fra c{e^5}{e^5}\right)^n$ = 1

5. thats wrong