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.