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B+4=(191/210+1)+(161/240+1)+(129/272+1)+(95/306+1)
B+4=401/210+401/240+401/272+401/306
B+4=401x(1/210+1/240+1/272+1/306)
B+4=401X 1/63
B=401/63-4
B=149/63
Hoc tot!
\(\frac{-2}{5}.\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{-2}{5}.\left(\frac{2}{17}+\frac{-2}{5}\right)\)
\(=\frac{-2}{5}.\frac{5}{17}-\frac{-2}{5}.\frac{3}{5}-\frac{-2}{5}.\frac{2}{17}-\frac{-2}{5}.\frac{-2}{5}\)
\(=\frac{-2}{5}.\left(\frac{5}{17}-\frac{2}{17}\right)-\frac{-2}{5}.\left(\frac{3}{5}+\frac{-2}{5}\right)\)
\(=\frac{-2}{5}.\frac{3}{17}-\frac{-2}{5}.\frac{1}{5}\)
\(=\frac{-2}{5}.\left(\frac{3}{17}-\frac{1}{5}\right)\)
\(=\frac{-2}{5}.\frac{-2}{85}\)
\(=\frac{4}{425}\)
\(\frac{-2}{5}.\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{-2}{5}.\left(\frac{2}{17}+\frac{-2}{5}\right)\)
= \(\frac{-2}{5}.\frac{-26}{85}-\frac{-2}{5}.\frac{-24}{85}\)
= \(\frac{-2}{5}.\left(\frac{-26}{85}-\frac{-24}{85}\right)\)
= \(\frac{-2}{5}.\frac{-2}{85}\)
= \(\frac{4}{425}\)
a/ \(A=\frac{1}{6}+\frac{1}{12}+.........+\frac{1}{56}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{4}\)
b/ \(B=\frac{5}{11.16}+\frac{5}{16.21}+........+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+........+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{5}{66}\)
a) \(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(A=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
b) \(B=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(B=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(B=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{72}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)
\(=\frac{1}{2}-\frac{1}{9}=\frac{9}{18}-\frac{2}{18}=\frac{7}{18}\)
dễ mà phân tích các mẫu ra là các tích của 2 số gần liên tiếp rồi áp dụng phân số ai cập thui