Toán Lớp 6: tính nhanh
1) q=6 mũ 0+6 mũ 1 + 6 mũ 2 +6 mũ3 +…..+6 mũ 99 +6 mũ 100
2)p=5 +5 mũ 2+5 mũ 3+…..+5 mũ 2021
3)T=8 mũ 0+8 mũ 1+8 mũ 2+8 mũ 3+……..+8 mũ 2010
4)R=9 + 9 mũ 2+9 mũ 3 +9 mũ 4 +……+9 mũ 2020 +9 mũ 2021
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Toán Lớp 6: tính nhanh
1) q=6 mũ 0+6 mũ 1 + 6 mũ 2 +6 mũ3 +…..+6 mũ 99 +6 mũ 100
2)p=5 +5 mũ 2+5 mũ 3+…..+5 mũ 2021
3)T=8 mũ 0+8 mũ 1+8 mũ 2+8 mũ 3+……..+8 mũ 2010
4)R=9 + 9 mũ 2+9 mũ 3 +9 mũ 4 +……+9 mũ 2020 +9 mũ 2021
Comments ( 1 )
1)\\
Q = {6^0} + {6^1} + {6^2} + … + {6^{99}} + {6^{100}}\\
\Leftrightarrow 6.Q = {6^1} + {6^2} + {6^3} + … + {6^{100}} + {6^{101}}\\
\Leftrightarrow 6Q – Q = 5Q = {6^{101}} – {6^0}\\
\Leftrightarrow 5Q = {6^{101}} – 1\\
\Leftrightarrow Q = \dfrac{{{6^{101}} – 1}}{5}\\
2)\\
P = 5 + {5^2} + {5^3} + … + {5^{2021}}\\
\Leftrightarrow 5P = {5^2} + {5^3} + {5^4} + … + {5^{2022}}\\
\Leftrightarrow 5P – P = 4P = {5^{2022}} – 5\\
\Leftrightarrow P = \dfrac{{{5^{2022}} – 5}}{4}\\
3)\\
T = {8^0} + {8^1} + {8^2} + …. + {8^{2010}}\\
\Leftrightarrow 8T = {8^1} + {8^2} + {8^3} + … + {8^{2011}}\\
\Leftrightarrow 8T – T = 7T = {8^{2011}} – {8^0}\\
\Leftrightarrow T = \dfrac{{{8^{2011}} – 1}}{7}\\
4)\\
R = 9 + {9^2} + {9^3} + {9^4} + …. + {9^{2020}} + {9^{2021}}\\
\Leftrightarrow 9R = {9^2} + {9^3} + {9^4} + … + {9^{2021}} + {9^{2022}}\\
\Leftrightarrow 9R – R = 8R = {9^{2022}} – 9\\
\Leftrightarrow R = \dfrac{{{9^{2022}} – 9}}{8}
\end{array}$