how do i turn this into indeterminate form infinity * 0

[calcnoob145]

do i divide everything by n and work from there

 

[Deleted member 4993]

View attachment 2800 do i divide everything by n and work from there

You do not tell us why do you want to convert the given expression to the form 0 * \(\displaystyle \infty\)

 

[pka]

View attachment 2800 do i divide everything by n and work from there

You should learn this very useful fact:
\(\displaystyle \displaystyle{\lim _{n \to \infty }}{\left( {1 + \frac{a}{{n + b}}} \right)^{cn}} = {e^{ac}}\)

Now put \(\displaystyle \dfrac{9n+4}{9n-4}\) into that form.

 

[lookagain]

View attachment 2800 do i divide everything by n and work from there

calcnoob145, the problem statement is wrong. There is no true equality there. There has to be \(\displaystyle "\displaystyle\lim_{n \to \infty}"\) in front of the expressions to the left side of the right-most equals sign. Or, (not only limited to) after the first equality, erase \(\displaystyle "= \ e^{\frac{8}{9}}" \ \) and write on the next line "\(\displaystyle \displaystyle\lim_{n \to \infty}a_n \ = \ e^{\frac{8}{9}}\)"