Classify whether the limit converges or diverges and if its bounded or unbounded $$\left\\{\frac{(-1)^n100^n}{n!}\right\\}$$ So, I know $\left\\{\frac{100^n}{n!}\right\\}$ is a basic null sequence, although here itll oscillate between negative and positive values dependent on the odd/even nature of $n$. However, I think it'll still converge to $0$ and be a null sequence eventually. and its also bounded. Am I wrong?

Squeeze theorem will do $$\frac{-100^n}{n!}\leq\frac{(-1)^n100^n}{n!}\leq \frac{100^n}{n!}$$ Both of which converge to zero.