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Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha
1, 7A = 7+7^2+7^3+....+7^2008
6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1
=> A = (7^2008-1)/6
Tk mk nha
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)
\(\Rightarrow6A=7^{2008}-1\)
\(\Rightarrow A=\frac{7^{2008}-1}{6}\)
a: \(=\left(-\dfrac{3}{4}+\dfrac{5}{13}\right)\cdot\dfrac{7}{2}-\left(\dfrac{5}{2}+\dfrac{8}{13}\right)\cdot\dfrac{7}{2}\)
\(=\dfrac{7}{2}\left(-\dfrac{3}{4}+\dfrac{5}{13}-\dfrac{5}{3}-\dfrac{8}{13}\right)\)
\(=\dfrac{7}{2}\cdot\dfrac{-413}{156}=\dfrac{-2891}{312}\)
b: \(=-\dfrac{3}{5}:\left(\dfrac{-2-5}{30}\right)+\dfrac{3}{5}:\left(-\dfrac{1}{3}-\dfrac{16}{15}\right)\)
\(=\dfrac{-3}{5}\cdot\dfrac{-30}{7}+\dfrac{3}{5}:\dfrac{-5-16}{15}\)
\(=\dfrac{3}{5}\cdot\dfrac{30}{7}+\dfrac{3}{5}\cdot\dfrac{-5}{7}\)
\(=\dfrac{3}{5}\cdot\dfrac{25}{7}=\dfrac{15}{7}\)
c: \(=3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)
\(=\left(3-5-6\right)+\left(\dfrac{-1}{4}+\dfrac{7}{4}-\dfrac{3}{2}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\dfrac{6}{5}\)
\(=-8+1+\dfrac{6}{5}=-7+\dfrac{6}{5}=\dfrac{-35+6}{5}=\dfrac{-29}{5}\)
a) 5 7 .
b) 0.
c) 1.
d) 0.