A = \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)

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

  \(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

B = \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

  \(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

  \(=1-\frac{1}{13}=\frac{12}{13}\)

\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

\(B=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

\(=1-\frac{1}{13}=\frac{12}{13}\)

A=\(\frac{1}{6}\)+\(\frac{1}{12}\)+......+\(\frac{1}{56}\)

A=\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+...+\(\frac{1}{7.8}\)

A=\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+....+\(\frac{1}{7}\)-\(\frac{1}{8}\)

A=\(\frac{1}{2}\)-\(\frac{1}{8}\)=\(\frac{3}{8}\)

B=\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+...+\(\frac{2}{11.13}\)

B=1-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+....+\(\frac{1}{11}\)-\(\frac{1}{13}\)

B=1-\(\frac{1}{13}\)=\(\frac{12}{13}\)

C=\(\frac{3}{4}\)+\(\frac{3}{28}\)+....+\(\frac{3}{304}\)

C=\(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+..+\(\frac{3}{16.19}\)

Rồi bạn cũng tách ra như câu A và câu B

a) \(\frac{30}{51}\)\(-\)\(\frac{20}{52}\)\(+\)\(\frac{14}{34}-\frac{56}{91}-2\)

\(=\frac{10}{17}-\frac{5}{13}+\frac{7}{17}-\frac{8}{13}-2\)

= (\(\frac{10}{17}\)\(+\frac{7}{17}\)) \(-\)(\(\frac{5}{13}+\frac{8}{13}\)) \(-2\)

= \(1-1-2\)

=\(0-2\)

= -2

k cho mik nha

3/14:1/28-13/21:1/28+29/42:-1/28-8

=3/14.28-13/21.28+29/42.(-28)-8

=3/14.28-13/21.28+-29/42.28-8

=(3/14-13/21+ -29/42).28-8

=-23/21.28-8

=-92/3-8=-116/3

động não tí đi

Bạn ko trả lời thì thôi bạn ấy ko biết thì mới hỏi

Ta có : \(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+...+\) \(\frac{1}{x^2+15x+56}=\frac{1}{14}\)

<=>\(\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}\)+...+ \(\frac{1}{\left(x+7\right)\left(x+8\right)}=\frac{1}{14}\)

<=> \(\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+...+\frac{1}{x+7}-\frac{1}{x+8}\)= \(\frac{1}{14}\)

<=> \(\frac{1}{x+1}-\frac{1}{x+8}=\frac{1}{14}\)

<=> \(\frac{x+8-x-1}{\left(x+1\right)\left(x+8\right)}=\frac{1}{14}\)

<=>\(\frac{7.14}{14\left(x+1\right)\left(x+8\right)}=\frac{\left(x+1\right)\left(x+8\right)}{14\left(x+1\right)\left(x+8\right)}\)

<=> \(x^2+9x+8=98\)<=> \(x^2+9x-90=0\)

<=> (x-6)(x+15) =0 

<=> \(\orbr{\begin{cases}x=6\\x=-15\end{cases}}\)

Vậy phương trình có 2 nghiệm  x  \(\in\left(6,15\right)\)

==============

- Do ko biết viết dấu ngoặc nhọn nên thay = dấu ngoặc tròn

- Đề ko rõ ràng , lần sau nhớ ghi yêu cầu ?  

a = 0

câu 2 khó quá

bn mà k cho mk thì đáp án sẽ hiện ra,thật đó

14*0=0

\(\frac{8}{23}\cdot\frac{46}{24}-x=\frac{1}{3}\)

=> \(\frac{2}{3}-x=\frac{1}{3}\)

=> \(x=\frac{1}{3}\)

\(\frac{10}{12}\div x=\frac{28}{9}\cdot\frac{3}{56}\)

=> \(\frac{10}{12}\div x=\frac{1}{6}\)

=> \(x=\frac{60}{12}=5\)

\(\frac{x-12}{4}=\frac{1}{2}\)

=> \(\left(x-12\right)\cdot2=4\cdot1\)

=> \(2x-24=4\)

=> \(2x=28\)

=> \(x=14\)

a) \(\frac{\frac{2}{3}+\frac{2}{7}-\frac{1}{14}}{-1-\frac{3}{7}+\frac{3}{28}}=\frac{\frac{37}{42}}{\frac{-37}{28}}=\frac{37}{42}.\frac{28}{-37}=\frac{-2}{3}\)

b) \(\left(x+\frac{1}{2}\right).\left(\frac{2}{3}-2x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0-\frac{1}{2}=\frac{-1}{2}\\x=\left(\frac{2}{3}-0\right):2=\frac{1}{3}\end{cases}}\)

Vậy \(x\in\left\{\frac{-1}{2};\frac{1}{3}\right\}\)

a,\(\frac{\frac{2}{3}+\frac{2}{7}-\frac{1}{14}}{-1-\frac{3}{7}+\frac{3}{28}}=\frac{2.\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{28}\right)}{3.\left(-\frac{1}{3}-\frac{3}{7}+\frac{1}{28}\right)}=\frac{-2}{3}\)

cách này k cần dùng máy tính (hok tốt)

b,\(\left(x+\frac{1}{2}\right).\left(\frac{2}{3}-2x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{1}{3}\end{cases}}}\)

Vậy....

\(\frac{5}{7}+\frac{5}{14}+\frac{5}{28}+\frac{5}{56}+\frac{5}{112}+\frac{5}{224}+\frac{5}{448}+\frac{5}{896}\)

\(=(\frac{5}{7}+\frac{5}{14})+(\frac{5}{28}+\frac{5}{56})+(\frac{5}{112}+\frac{5}{224})+(\frac{5}{448}+\frac{5}{896})\)

\(=\frac{15}{14}+\frac{15}{56}+\frac{15}{224}+\frac{15}{896}\)

\(=(\frac{15}{14}+\frac{15}{224})+(\frac{15}{56}+\frac{15}{896})\)

\(=\frac{255}{224}+\frac{255}{896}=\frac{1275}{896}\)

Rồi tự rút gọn nhé . Nếu số đó ko rút gọn được thì giữ nguyên

Chúc bạn học tốt :>