Answer
$0$.
Work Step by Step
We have
$$ \lim\limits_{n \to \infty}{b_n}=\lim\limits_{n \to \infty} e^{1-n^2}=0.$$
Where we used the fact that $\lim_{x\to \infty } e^{-x}=\infty$ when $x\gt 0$. Using Theorem 1, we see that the sequence $b_n$ converges to $0$.
