\(a,\)\(x+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)

  \(x+\left(\frac{9-5}{5.9}+\frac{13-9}{9.13}+\frac{17-13}{13.17}+...+\frac{45-41}{41.45}\right)=-\frac{37}{45}\)

  \(x+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+....+\frac{1}{41}-\frac{1}{45}\right)-\frac{37}{45}\)

 \(x+\left(\frac{1}{5}-\frac{1}{45}\right)=-\frac{37}{45}\)

 \(x+\frac{8}{45}=-\frac{37}{45}\)

\(x=-\frac{37}{45}-\frac{8}{45}\)

\(x=-1\)

thế phần b, c đâu bạn

a) gt \(\Leftrightarrow\) s-\(10\times\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{53\times55}\right)=\frac{3}{11}\)

\(\Leftrightarrow s-10\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow S-10\times\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow S=1\)

câu b hình như sai đề

Phải là \(\frac{1}{36}\) chứ ko phải \(\frac{1}{39}\)

ukm 1/36

<=> x\(-10\left(\frac{1}{11x13}+\frac{1}{13x15}+...+\frac{1}{53x55}\right)\)) =\(\frac{3}{11}\)

x\(-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

X-10\(\left(\frac{1}{11}-\frac{1}{55}\right)\)=\(\frac{3}{11}\)

X-\(\frac{40}{55}\)=\(\frac{3}{11}\)

X=\(\frac{3}{11}+\frac{40}{55}=\frac{15+40}{55}=\frac{55}{55}=1\)

Sửa đề : \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Leftrightarrow\)\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Leftrightarrow\)\(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)

\(\Leftrightarrow\)\(2\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)

\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}.\frac{1}{2}\)

\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)

\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{18}\)

\(\Leftrightarrow\)\(x+1=18\)

\(\Leftrightarrow\)\(x=18-1\)

\(\Leftrightarrow\)\(x=17\)

Vậy \(x=17\)

Chúc bạn học tốt ~ 

\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(\Leftrightarrow\)\(x+10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)

\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow\)\(x+10.\frac{4}{55}=\frac{3}{11}\)

\(\Leftrightarrow\)\(x+\frac{40}{55}=\frac{3}{11}\)

\(\Leftrightarrow\)\(x=\frac{3}{11}-\frac{40}{55}\)

\(\Leftrightarrow\)\(x=\frac{-5}{11}\)

Vậy \(x=\frac{-5}{11}\)

Chúc bạn học tốt ~ 

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Rightarrow\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+\frac{2}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Rightarrow2\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)

\(\Rightarrow2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\Rightarrow2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\Rightarrow\frac{1}{3}-\frac{2}{x+1}=\frac{2}{9}\)

\(\Rightarrow\frac{2}{x+1}=\frac{1}{9}\)

=> 2.9 = x + 1

=> x + 1 = 18

=> x = 17

\(\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{19\times21}\right)\times462-2,04\div\left(x+15\right)+11,02=30\)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\times462-2,04\div\left(x+15\right)+11,02=30\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)\times462-2,04\div\left(x+15\right)=30-11,02\)

\(\frac{10}{231}\times462-2,04\div\left(x+15\right)=18,98\)

\(20-2,04\div\left(x+15\right)=18,98\)

\(2,04\div\left(x+15\right)=20-18,98\)

\(2,04\div\left(x+15\right)=1,02\)

\(x+15=2,04\div1,02\)

\(x+15=2\)

\(x=2-15\)

\(x=-13\)

Ta có : \(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)642-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)

=> \(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)642-0,04:\left(x+1,05\right):0,12=19\)

=> 

(nãy bấm nhầm) tiếp nà :

=> \(\left(\frac{1}{11}-\frac{1}{21}\right)462-0,04:\left(x+1,05\right):0,12=19\)

=> \(\frac{10}{231}.462-0,04:\left(x+1,05\right):0,12=19\)

=> \(20-0,04:\left(x+1,05\right):0,12=19\)

=> 0,04 : (x + 1,05) : 0,12 = 1

=> 0,04 : (x + 1,05) = 0,12

=> \(x+1,05=\frac{1}{3}\) 

=> \(x=\frac{1}{3}-1,05=...\)

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)562-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)

\(\Rightarrow2.\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)462-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right)462-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)

\(\Rightarrow\frac{10}{231}.462-\left[0,04:\left(x+1,05\right)\right]:0,12=19\)

\(\Rightarrow20-\left[0,04:\left(x+1,05\right)\right]0,12=19\)

\(\Rightarrow\left[0,04:\left(x+1,05\right)\right]:0,12=20-19=1\)

\(\Rightarrow0,04:\left(x+1,05\right)=1.0,12=0,12\)

\(\Rightarrow x+1,05=0,04:0,12=\frac{1}{3}\)

\(\Rightarrow x=\frac{1}{3}-1,05=\frac{1}{3}-\frac{105}{100}=-\frac{43}{60}\)

(Làm vậy đúng không?)