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…?
$$\left(1+\left(\frac1\infty\right)^2\right)^\infty = (1+0)^\infty = 1$$

In short no. If you look at the limit that yields $e$ And did the same trick what would you get?
$$
\lim_{n \to \infty}\left(1+\frac{1}{n}\right)^n = e\neq \left(1+\frac{1}{\infty}\right)^\infty = 1
$$
The last equality is more to match with your statement question than being a proper definition of 1. 
