Tính tổng sau đây: C 0 2021 - 2C 1 2021 + 2^2C 2 2021 - 2^3C 3 2021...

$C_{2021}^0-2C_{2021}^1+2^2{C}_{2021}^2-2^3{C}_{2021}^3+\dots -2^{2021}{C}_{2021}^{2021}$

$=C_{2021}^0+C_{2021}^1\left(-2\right)+C_{2021}^2{\left(-2\right)}^2+C_{2021}^3{\left(-2\right)}^3+\dots +C_{2021}^{2021}{\left(-2\right)}^{2021}$

$=C_{2021}^0{1}^{2021}+C_{2021}^1{1}^{2020}\left(-2\right)+C_{2021}^2{1}^{2019}{\left(-2\right)}^2+C_{2021}^3{1}^{2018}{\left(-2\right)}^3+\dots +C_{2021}^{2021}{\left(-2\right)}^{2021}$