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

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

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

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

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

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

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

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

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

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

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

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

\(x=\frac16:\frac23\)

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

vậy \(x=\frac14\)

\(x\cdot\left(2+x\right)\cdot\left(7-x\right)=0\\ =>\left[{}\begin{matrix}x=0\\2+x=0\\7-x=0\end{matrix}\right.\\ =>\left[{}\begin{matrix}x=0\\x=-2\\x=7\end{matrix}\right.\)

vậy phương trình có 3 nghiệm là \(x_1=0;x_2=-2;x_3=7\)

Th 1 : x + 2 = 0 x = 0 - 2 x = -2 Th 2 : x - 7 = 0 x = 0 + 7 x = 7

\(-\dfrac{5}{15}+\dfrac{9}{7}+\dfrac{1}{-3}-\left(-\dfrac{276}{14}\right)\\ =-\dfrac{5}{15}+\dfrac{18}{14}-\dfrac{5}{15}+\dfrac{276}{14}\\ =-\dfrac{10}{15}+\dfrac{294}{14}=-\dfrac{2}{3}+21=\dfrac{61}{3}\)

- \(\frac{5}{15}\) + \(\frac97\) + \(\frac{1}{-3}\) - \(-\frac{276}{14}\)

= (- \(\frac13\) - \(\frac13\)) + (\(\frac97\) + \(\frac{138}{7}\))

= - \(\frac23\) + 21

= - \(\frac23+\frac{63}{3}\)

= \(\frac{61}{3}\)

A=1.2+2.3+3.4+4.5+...+2013.2014
3A=1.2.3+2.3.3+3.4.3+...+2013.2014.3
3A=1.2.3+2.3(4-1)+3.4(5-2)+...+2013.2014(2015-2012)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2013.2014.2015-2012.2013.2014
3A=2013.2014.2015

A=\(\dfrac{2013.2014.2015}{3}\)

Chúc bạn học tốt nhé!

8 giờ = 8/1 giờ

14 giờ = 14/1 giờ