Proof that $\lim_{n\to\infty} n\left(\frac{1}{2}\right)^n = 0$ Please show how to prove that $$\lim_{n\to\infty} n\left(\frac{1}{2}\right)^n = 0$$

With Stolz-Cesaro Theorem :
$$
\color{#66f}{\large\lim_{n \to \infty}{n \over 2^{n}}}
=\lim_{n \to \infty}{\left(n + 1\right) - n \over 2^{n + 1} - 2^{n}}
=\lim_{n \to \infty}{1 \over 2^{n}}=\color{#66f}{\Large 0}
$$
