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\(2\frac{3}{4}+1\frac{5}{6}+3\frac{1}{4}+2\frac{1}{6}\)
= \(\frac{11}{4}+\frac{11}{6}+\frac{13}{4}+\frac{13}{6}\)
= \(\left(\frac{11}{4}+\frac{13}{4}\right)+\left(\frac{11}{6}+\frac{13}{6}\right)\)
= \(\frac{24}{4}+\frac{24}{6}\)
= \(6+4\)
= \(10\)
Tôi đặt S cho nhanh, đừng hỏi tại sao còn bạn chứ là A nhé :))
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)\)
\(=1+2+2\)
\(=5\)
\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}=\frac{1}{6}\)
\(\frac{3}{5×3}+\frac{3}{5×7}+\frac{3}{7×9}+\frac{3}{9×11}+\frac{3}{11×13}\)
\(=\frac{3}{2}×\left(\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+\frac{2}{9×11}+\frac{2}{11×13}\right)\)
\(=\frac{3}{2}×\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{3}{2}×\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{3}{2}×\left(\frac{13}{39}-\frac{3}{39}\right)\)
\(=\frac{3}{2}×\frac{10}{39}\)
\(=\frac{5}{13}\)
\(\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+\frac{3}{11.13}\)
\(=\frac{3}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{ 1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11} +\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{3}{2}.\frac{10}{39}\)
\(=\frac{15}{39}\)
1/2 x (6/1-6/3+6/3-6/5+ ... +6/37-6/39)
1/2 x (6/1-6/39)
1/2 x 228/39
228/78
\(\frac{6}{1\cdot3}+\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{35.37}+\frac{6}{37.39}\)
\(=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{37}-\frac{1}{39}\right)\)
\(=3\left(1-\frac{1}{39}\right)=3\cdot\frac{38}{39}=\frac{114}{39}\)
Ps: Bạn tự rút gọn nhé!!!