Áp dụng công thức : $\dfrac{k}{n}C_n^k = C_{n-1}^{k-1}$
$\to S=C_{2020}^1+2C_{2020}^2+.....+2020C_{2020}^{2020} = 2020.(\dfrac{1}{2020}. C_{2020}^1+\dfrac{2}{2020}.C_{2020}^2+...+\dfrac{2020}{2020}C_{2020}^{2020})$
$= 2020.(C_{2020-1}^0 + C_{2020-1}^1 +... +C_{2020-1}^{2020-1})$
$=2020.2^{2019}$