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45 x 16 - 17 =45 x (15+1) -17 = 45 x 15 +45 -17 =45 x 15 +28 =1
45 x 15 +28 GIỮ NGUYÊN = giữ nguyên = giữ nguyên
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)
a) Ta có: \(A=\frac{3535.232323}{353535.2323}=\frac{35.101.23.10101}{35.10101.23.101}=\frac{35}{23}\)
\(B=\frac{3535}{3434}=\frac{35.101}{34.101}=\frac{35}{34}\)
\(C=\frac{2323}{2322}=\frac{2323}{2322}\)
\(a,16,88+9,76+3,12-5,13\)
\(=\left(16,88+3,12\right)+\left(9,76-5,13\right)\)
\(=20+4,63\)
\(=24,63\)
\(b,\frac{19}{11}+\frac{8}{13}+\frac{3}{11}\)
\(=\left(\frac{19}{11}+\frac{3}{11}\right)+\frac{8}{13}\)
\(=2+\frac{8}{13}\)
\(=\frac{34}{13}\)
\(c,\frac{1}{2}\div\frac{1}{4}-\frac{1}{6}\)
\(=2-\frac{1}{6}\)
\(=\frac{11}{6}\)
\(A=11\frac{2}{1.3}+11\frac{2}{3.5}+11\frac{2}{5.7}+11\frac{2}{7.9}+11\frac{2}{9.11}\)
\(A=11+\frac{2}{1.3}+11+\frac{2}{3.5}+11+\frac{2}{5.7}+11+\frac{2}{7.9}+11+\frac{2}{9.11}\)
\(A=55+\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(A=55+\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(A=55+\frac{1}{1}-\frac{1}{11}\)
\(A=56-\frac{1}{11}\)
\(A=\frac{616}{11}-\frac{1}{11}=\frac{615}{11}\)
Vậy A = 615 / 11
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}=\frac{1}{7}\)
\(N=\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+...+\frac{1}{2005.2010}\)
\(N=\frac{1}{5}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{2005}-\frac{1}{2010}\right)\)
\(N=\frac{1}{5}.\left(1-\frac{1}{2010}\right)\)
\(N=\frac{1}{5}.\frac{2009}{2010}\)
\(N=\frac{2009}{10050}\)
b. 26,7