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Xét khai triển:
\(2^{2021}=\left(1+1\right)^{2021}=C_{2021}^0+C_{2021}^1+...+C_{2021}^{2020}+C_{2021}^{2021}\) (1)
\(0=\left(1-1\right)^{2021}=C_{2021}^0-C_{2021}^1+C_{2021}^2+...+C_{2021}^{2020}-C_{2021}^{2021}\) (2)
Trừ vế cho vế (1) và (2):
\(2^{2021}=2.C_{2021}^1+2.C_{2021}^3+...+2C_{2021}^{2021}\)
\(\Rightarrow C_{2021}^1+C_{2021}^3+...+C_{2021}^{2019}+C_{2021}^{2021}=\dfrac{2^{2021}}{2}=2^{2020}\)
\(\Rightarrow C_{2021}^1+C_{2021}^3+...+C_{2021}^{2019}+1=2^{2020}\)
\(\Rightarrow C_{2021}^1+C_{2021}^3+...+C_{2021}^{2019}=2^{2020}-1\)
(2021 - 13) - (2021 + 11) = 2021 - 13 - 2021 - 11 = (2021 - 2021) - ( 13 + 11 ) = 0 + ( - 24) = -24
Ta có:\(\left(2021-13\right)-\left(2021+11\right)\)
\(=2021-13-2021-11\)
\(=-13-11\)
\(=-24\)
2021+2021+2021+2021+2021-2021*4
= 2021*1 2021*1 2021*1 2021*1 2021*1 - 2021*4
= 2021(1+1+1+1+1-4)
= 2021*1
= 2021
2021+2021+2021+2021+2021-2021x4
= 2021 x 5 - 2021 x 4
= 2021 x (5 - 4)
= 2021 x 1
= 2021