\(\dfrac{4}{3.5}+\dfrac{8}{5.9}+\dfrac{12}{9.15}+...+\dfrac{32}{x\left(x+16\right)}=\dfrac{16}{15}\)

\(2.\left(\dfrac{2}{3.5}+\dfrac{4}{5.9}+\dfrac{6}{9.15}+..+\dfrac{16}{X.\left(X+16\right)}\right)=\dfrac{16}{15}\)

\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{15}+...+\dfrac{1}{X}-\dfrac{1}{X+16}=\dfrac{8}{15}\)

\(\dfrac{1}{X+16}=\dfrac{1}{3}-\dfrac{8}{15}\)

\(\dfrac{1}{X+16}=\dfrac{-1}{5}\)

\(X+16=-5\)

\(X=-21\)

\(\frac{4}{3.5}+\frac{8}{5.9}+\frac{12}{9.15}+...+\frac{32}{n\left(n+16\right)}=\frac{16}{25}\)

\(2\left(\frac{1}{3}-\frac{1}{5}\right)+2\left(\frac{1}{5}-\frac{1}{9}\right)+2\left(\frac{1}{9}-\frac{1}{15}\right)+...+2\left(\frac{1}{n}-\frac{1}{n+16}\right)=\frac{16}{25}\)

\(2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{15}+...+\frac{1}{n}-\frac{1}{n+16}\right)=\frac{16}{25}\)

\(2\left(\frac{1}{3}-\frac{1}{n+16}\right)=\frac{16}{25}\)

\(\frac{1}{3}-\frac{1}{n+16}=\frac{8}{25}\)

\(\frac{1}{n+16}=\frac{1}{75}\)

\(\Rightarrow n+16=75\)

\(\Rightarrow n=59\)

bạn  Thanh Tùng DZ mình vẫn chưa hiểu tại sao \(\dfrac{8}{5.9}\) = 2.(\(\dfrac{1}{5}\) - \(\dfrac{1}{9}\)) 

\(M=\frac{1}{3.4}+\frac{7}{3.4}+\frac{2}{3.5}+\frac{14}{5.9}-\frac{4}{9.13}=\frac{8}{3.4}+\frac{2}{3.5}+\frac{2}{9}\left(\frac{7}{5}-\frac{2}{13}\right)\)

=> \(M=\frac{2}{3}+\frac{2}{3.5}+\frac{2}{9}.\frac{81}{5.13}=\frac{2}{3}\left(1+\frac{1}{5}\right)+\frac{18}{5.13}\)

=> \(M=\frac{2}{3}.\frac{6}{5}+\frac{18}{5.13}=\frac{4}{5}+\frac{18}{5.13}=\frac{2}{5}\left(2+\frac{9}{13}\right)=\frac{2}{5}.\frac{35}{13}\)

=> \(M=\frac{14}{13}\)

\(\dfrac{-8}{15}.\dfrac{3}{7}.\dfrac{15}{-8}.14=\left(\dfrac{-8}{15}.\dfrac{15}{-8}\right).\left(\dfrac{3}{7}.14\right)=1.6=6\)

\(\dfrac{17}{27}.\dfrac{13}{9}-\dfrac{4}{9}.\dfrac{17}{27}=\dfrac{17}{27}.\left(\dfrac{13}{9}-\dfrac{4}{9}\right)=\dfrac{17}{27}.1=\dfrac{17}{27}\)

1727.139−49.1727=1727.(139−49)=1727.1=1727

Ta có: \(\left(\frac{8}{1.9}+\frac{8}{9.17}+\frac{8}{17.25}+...+\frac{8}{49.57}\right)+2\left(x-1\right)=\frac{2x+7}{3}+\frac{5x-8}{4}\)

\(\Leftrightarrow1-\frac{1}{9}+\frac{1}{9}-\frac{1}{17}+\frac{1}{17}-\frac{1}{25}+....+\frac{1}{49}-\frac{1}{57}+2x-2=\frac{8x+28+15x-24}{12}\)

\(\Leftrightarrow1-\frac{1}{57}+2x-2=\frac{23x+4}{12}\)

\(\Leftrightarrow2x-\frac{58}{57}=\frac{23x+4}{12}\)

\(\Leftrightarrow24x-\frac{232}{19}=23x+4\)

\(\Leftrightarrow x=\frac{308}{19}\)

Đề bài yêu cầu gì?

bài 1

\(2A=\left(\frac{5}{1\cdot3}+\frac{5}{3\cdot5}+...+\frac{5}{99\cdot101}\right)\cdot2\)

\(=5\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{99\cdot101}\right)\)

\(=5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=5\left(1-\frac{1}{101}\right)\)

\(=5\cdot\frac{100}{101}\)

\(=\frac{500}{101}\Rightarrow A=\frac{500}{101}:2=\frac{250}{101}\)

bài 2:

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

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

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

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

\(x=\frac{-45}{45}=-1\)

thấy chưa huj nãy nói sai mà

Ta có: \(\frac{8}{1.9}+\frac{8}{9.17}+...+\frac{8}{49.57}=1-\frac{1}{9}+\frac{1}{9}-\frac{1}{17}+...+\frac{1}{49}-\frac{1}{57}=1-\frac{1}{57}=\frac{56}{57}\)

Vậy: 56/57 + 58/57 + 2x - 2 = 2x + 7/3 + 5x - 8/4

        2 + 2x - 2 = 2x + 7/3 + 5x - 8/4

   2x = 2x + 7/3 + 5x - 8/4

=> 7/3 + 5x - 8/4 = 0

1/3 + 5x = 0

=> 5x = -1/3

=> x = -1/3 : 5=-1/15

hỏi gì nhiều thế