Prove that $ \sum_{n=0}^{\infty} 2^{-n(n+1)/2} = \prod_{k=1}^{\infty} (1 - \frac{1}{2^k})^{(-1)^k}$

Question

Prove the following equality:

$$ \sum_{n=0}^{\infty} 2^{-n(n+1)/2} = \prod_{k=1}^{\infty} (1 - \frac{1}{2^k})^{(-1)^k}$$