Bài 5
S=\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+\dfrac{2}{10.13}+\dfrac{2}{13.16}\)
S=\(\dfrac{2}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+\dfrac{2}{13.16}\right)\)
S=\(\dfrac{2}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{16}\right)\)
S=\(\dfrac{2}{3}.\left(1-\dfrac{1}{16}\right)\)
S=\(\dfrac{2}{3}.\dfrac{15}{16}=\dfrac{5}{6}\)
23.(31.4+34.7+37.10+310.13+213.16)23.(31.4+34.7+37.10+310.13+213.16)
23.(1−116)23.(1−116)
Bài 5:
Ta có: \(S=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}+\dfrac{2}{10\cdot13}+\dfrac{2}{13\cdot16}\)
\(=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}\right)\)
\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{15}{16}=\dfrac{5}{8}\)
