Toán Lớp 7: (-1/7)^0+(-1/7)^1+(-1/7)^2+…+(-1/7)^2017
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Toán Lớp 7: (-1/7)^0+(-1/7)^1+(-1/7)^2+…+(-1/7)^2017
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A = {\left( { – \dfrac{1}{7}} \right)^0} + {\left( { – \dfrac{1}{7}} \right)^1} + {\left( { – \dfrac{1}{7}} \right)^2} + … + {\left( { – \dfrac{1}{7}} \right)^{2017}}\\
\Leftrightarrow – \dfrac{1}{7}.A = {\left( { – \dfrac{1}{7}} \right)^1} + {\left( { – \dfrac{1}{7}} \right)^2} + {\left( { – \dfrac{1}{7}} \right)^3} + … + {\left( { – \dfrac{1}{7}} \right)^{2018}}\\
\Leftrightarrow A – \left( {\dfrac{{ – 1}}{7}A} \right) = {\left( { – \dfrac{1}{7}} \right)^0} – {\left( { – \dfrac{1}{7}} \right)^{2018}}\\
\Leftrightarrow \dfrac{8}{7}A = 1 – \dfrac{1}{{{7^{2018}}}}\\
\Leftrightarrow A = \dfrac{7}{8}.\dfrac{1}{{{{8.7}^{2017}}}}
\end{array}$