1; 2; 5; 14; 41;...
giups mình với =((
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\(\dfrac{6}{16}-\dfrac{10}{64}=\dfrac{6\cdot4-10}{64}=\dfrac{14}{64}=\dfrac{7}{32}\)
\(C=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\)
\(3C=1-\dfrac{2}{3}+\dfrac{3}{3^2}-\dfrac{4}{3^3}+...+\dfrac{99}{3^{98}}-\dfrac{100}{3^{99}}\)
\(C+3C=1-\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{98}}-\dfrac{1}{3^{99}}-\dfrac{100}{3^{100}}\)
\(4C=1-\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+...+\dfrac{1}{3^{98}}-\dfrac{1}{3^{99}}-\dfrac{100}{3^{100}}\)
\(12C=3-1+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^{97}}-\dfrac{1}{3^{98}}-\dfrac{100}{3^{99}}\)
\(4C+12C=3-\dfrac{101}{3^{99}}-\dfrac{100}{3^{100}}\)
\(16C=3-\dfrac{101}{3^{99}}-\dfrac{100}{3^{100}}< 3\)
\(\Rightarrow C< \dfrac{3}{16}\)
\(C=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
\(\Rightarrow2C=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)
\(\Rightarrow2C+C=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)\)
\(\Rightarrow3C=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+2^{98}-2^{97}-....+2^2-2\)
\(=2^{101}-\left(2^{100}-2^{100}\right)+\left(2^{99}-2^{99}\right)-\left(2^{98}-2^{98}\right)+...+\left(2^3-2^3\right)-\left(2^2-2^2\right)-2\)
\(=2^{101}-2\)
\(\Rightarrow C=\dfrac{2^{101}-2}{3}\)
câu hỏi của bạn là gì
what is the 8th number in the sequence with pattern below