Limits and exponentials Asked to find $\lim_{n\to\infty}a_n$ where
$$a_n = \left(1+\dfrac1{n^2}\right)^n$$
I know that the limit = 1, and can get to this by saying $\ln a_n=n\ln\left(1+\dfrac1{n^2}\right)$ and going from there.
My question is: would it also be enough to simply direct substitute and say that…?
$$\left(1+\left(\frac1\infty\right)^2\right)^\infty = (1+0)^\infty = 1$$

This is precisely because $1^\infty$ is an indeterminate form.
See this very relevant question.
User's 'Blue' comment:

"Consider the purpose of the list of indeterminate forms. (Barring pathologies...) The first thing to try in an $x\to a$ limit is to "plug in" $a$ for $x$; if you get an expression that evaluates to $3$ or $\sqrt{\pi}$ or even $-\infty$, you're done.
The "indeterminate forms" are labels (and/or warnings) for cases where there's more work to do. They capture the essence of the problem and guide you to appropriate follow-up strategies ."

Also see the most upvoted and accepted answer there.
