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A=1/1.6+1/3.10+1/5.14+..........+1/41.86
A=1/2(1/1.3+1/3.5+1/5.7+.............+1/41.43)
A=1/2(1-1/3+1/3-1/5+1/5-1/7+..............+1/41-1/43)
A=1/2(1-1/43)
A=1/2*42/43=21/43
HỌC TỐT NHÉ!!!
\(B=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....++\frac{1}{9}-\frac{1}{10}\)
\(B=1-\frac{1}{10}=\frac{9}{10}\)
\(C=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(C=1-\frac{1}{100}\)
\(C=\frac{99}{100}\)
\(A=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}\right):5\)
\(A=\left(1-\frac{1}{501}\right):5\)
\(A=\frac{500}{501}:5=\frac{100}{501}\)
Ta có : \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right) \)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(\Rightarrow\) \(A=\frac{1}{5}.\frac{501-1}{501}=\frac{1}{5}.\frac{500}{501}\)
\(\Rightarrow\) \(A=\frac{1.500}{5.501}=\frac{20}{1.501}=\frac{20}{501}\)
Vậy \(A=\frac{20}{501}\)
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(S=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(S=5.\left(1-\frac{1}{31}\right)\)
\(S=5.\frac{30}{31}\)
\(S=\frac{150}{31}\)
Câu L bạn thiếu số\(\frac{1}{475}\)
\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)
\(L=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)
\(L=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\right)\)
\(L=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\right)\)
\(L=\frac{1}{6}.\left(1-\frac{1}{37}\right)\)
\(L=\frac{1}{6}.\frac{36}{37}\)
\(L=\frac{6}{37}\)
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(=5\left[\left(1-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+...+\left(\frac{1}{26}-\frac{1}{31}\right)\right]\)
\(=5\left[1-\frac{1}{31}\right]\)
\(=5.\frac{30}{31}=\frac{150}{31}\)
\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{775}+\frac{1}{1147}\)
\(L.6=\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}\)
\(L.6=\left(1-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{19}\right)+\left(\frac{1}{19}-\frac{1}{25}\right)+\left(\frac{1}{25}-\frac{1}{31}\right)\)
\(L.6=1-\frac{1}{31}\)
\(L.6=\frac{31}{31}-\frac{1}{31}\)
\(L.6=\frac{25}{31}\)
\(L=\frac{30}{31}:6\)
\(L=\frac{30}{31}.\frac{1}{6}\)
\(L=\frac{30}{186}\)
\(A=\frac{1}{1.2.3}+\frac{1}{3.2.5}+\frac{1}{5.2.7}+\frac{1}{7.2.9}+...+\frac{1}{41.2.43}\)
\(4A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{41.43}\)
\(4A=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{43-41}{41.43}\)
\(4A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{41}-\frac{1}{43}=1-\frac{1}{43}\)
\(A=\frac{1}{4}-\frac{1}{172}=\frac{42}{172}=\frac{21}{86}\)