Toán Lớp 11: Tính tổng:
$C^{0}_{2021}$ + $2C^{1}_{2021}$ + $2^{2}$$C^{2}_{2021}$+…+$2^{2021}$$C^{2021}_{2021}$
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Toán Lớp 11: Tính tổng:
$C^{0}_{2021}$ + $2C^{1}_{2021}$ + $2^{2}$$C^{2}_{2021}$+…+$2^{2021}$$C^{2021}_{2021}$
Comments ( 1 )
C_{2021}^0 + 2C_{2021}^1 + {2^2}C_{2021}^2 + … + {2^{2021}}C_{2021}^{2021}\\
{\left( {1 + x} \right)^{2021}} = C_{2021}^0 + C_{2021}^1.x + C_{2021}^2{x^2} + … + {x^{2021}}C_{2021}^{2021}\\
x = 2 \Rightarrow {\left( {1 + 2} \right)^{2021}} = C_{2021}^0 + C_{2021}^1.2 + C_{2021}^2{2^2} + … + {2^{2021}}C_{2021}^{2021}\\
\Rightarrow C_{2021}^0 + C_{2021}^1.2 + C_{2021}^2{2^2} + … + {2^{2021}}C_{2021}^{2021} = {3^{2021}}
\end{array}$