$\lim_{n \to \infty} (1-p)^n$ when $X = 0$

Question

Could someone explain the following please:

Expanding $(1-p)^n$ using the maclaurin does not tend to zero as $n \to \infty$ Could someone enlighten me as to how this happens?

Answer 1

For any $r \in [0,1)$ the series $\sum r^{n}$ is a convergent geometric series. In particular $r^{n} \to 0$ as $n \to \infty$. Take $r=1-p$.