\(C=3\cdot\dfrac{1}{1\cdot2}-5\cdot\dfrac{1}{2\cdot3}+7\cdot\dfrac{1}{3\cdot4}-...+15\cdot\dfrac{1}{7\cdot8}-17\cdot\dfrac{1}{8\cdot9}\)

\(=\dfrac{3}{1\cdot2}-\dfrac{5}{2\cdot3}+\dfrac{7}{3\cdot4}-...+\dfrac{15}{7\cdot8}-\dfrac{17}{8\cdot9}\)

\(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-...+\dfrac{1}{7}+\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{9}\)

\(=1-\dfrac{1}{9}=\dfrac{8}{9}\)

2601

\(\dfrac{2x+5}{n-3}=\dfrac{n-3+n-3+11}{n-3}\\ =\dfrac{n-3}{n-3}+\dfrac{n-3}{n-3}+\dfrac{11}{n-3}=1+1+\dfrac{11}{n-3}\)

để phân số này đạt giá trị nguyên thì n - 3 ∈ Ư(11) = {\(\pm1;\pm11\)}

\(n-3=1=>n=4\\ n-3=-1=>n=2\\ n-3=11=>n=14\\ n-3=-11=>n=-8\)

vậy n ∈ {4; 2; 14; -8} thì phân số có giá trị nguyên

Tra gg

\(\dfrac{1}{2}-\left[\dfrac{2}{3}x\cdot\left(-\dfrac{1}{3}\right)\right]=\dfrac{2}{3}\\ \dfrac{2}{3}x\cdot\left(-\dfrac{1}{3}\right)=-\dfrac{1}{6}\\ \dfrac{2}{3}x=\dfrac{1}{2}=>x=\dfrac{3}{4}\)

\(\frac12\) - (\(\frac23\) \(\times\) \(x\) - \(\frac13\)) = \(\frac23\)

\(\frac23\times\) \(x\) - \(\frac13\) = \(\frac12\) - \(\frac23\)

\(\frac23\times\) \(x\) = \(\frac13\) - \(\frac23+\frac12\)

\(\frac23\times\) \(x\) = - \(\frac13\) + \(\frac12\)

\(\frac23\) \(\times\) \(x\) = - \(\frac26+\frac36\)

\(\frac23\times\) \(x\) = \(\frac16\)

\(x=\frac16:\frac23\)

\(x\) = \(\frac14\)

vậy \(x=\frac14\)