Toán Lớp 6: Tính giá trị biểu thức:
B= $2^{2020}$ -$2^{2019}$ -$2^{2018}$ -..-$2^{2}$ -2-1
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Toán Lớp 6: Tính giá trị biểu thức:
B= $2^{2020}$ -$2^{2019}$ -$2^{2018}$ -..-$2^{2}$ -2-1
Comments ( 2 )
B = {2^{2019}} – {2^{2018}} – {2^{2017}} – {2^{2016}} – …. – 2 – 1\\
A = {2^{2018}} + {2^{2017}} + {2^{2016}} + …. + 2 + 1\\
\Leftrightarrow 2A = {2^{2019}} + {2^{2018}} + {2^{2017}} + …. + {2^2} + 2\\
\Rightarrow 2A – B = \left( {{2^{2019}} + {2^{2018}} + {2^{2017}} + …. + {2^2} + 2} \right) – \left( {{2^{2018}} + {2^{2017}} + {2^{2016}} + …. + 2 + 1} \right)\\
\Leftrightarrow A = {2^{2019}} – 1\\
\Rightarrow B = {2^{2019}} – m = {2^{2019}} – \left( {{2^{2019}} – 1} \right) = 1\\
B = {3^n} + {2^n} + {2020^n} = 3 + 2 + 2020 = 2025
\end{array}\)