Tính tổng $S = C_{2019}^1 + C_{2019}^2 + ... + C_{2019}^{2018}$.

Ta có: $S = C_{2019}^1 + C_{2019}^2 + ... + C_{2019}^{2018}$

$\Rightarrow S + C_{2019}^0 + C_{2019}^{2019} = C_{2019}^0 + C_{2019}^1 + C_{2019}^2 + ... + C_{2019}^{2018} + C_{2019}^{2019}$

⇔ S + 1 + 1 = (1 + 1)²⁰¹⁹

⇔ S = 2²⁰¹⁹ – 2.