Find $\sum_{n=-\infty}^{\infty} (0.5)^n$ We have: $$L=\lim_{n\to\infty} \sum_{k=-n}^n \frac1{2^k}.$$ The limit surely diverges or tends to $\infty.$ But I can't think of a proper way to show this.
Please suggest, how can I show that $L=\infty\,?$ Thanks in advance.

$$\sum_{k=-n}^n\frac1{2^k}\ge2^n$$
just by the term $k=-n$.
