\(\Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{29}{45}\left(x\ne0\right)\\ \Rightarrow\dfrac{7}{x}+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}+\dfrac{8}{45}=\dfrac{29}{45}\\ \Rightarrow\dfrac{7}{x}=\dfrac{21}{45}\Rightarrow\dfrac{21}{3x}=\dfrac{21}{45}\Rightarrow3x=45\\ \Rightarrow x=15\)

\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)

\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)

\(S=\frac{1}{4}\times\left(\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+...+\frac{4}{41\times45}\right)\)

\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)\)

\(S=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{45}\right)\)

\(S=\frac{1}{4}\times\frac{8}{45}\)

\(S=\frac{1\times2}{1\times45}\)

\(S=\frac{2}{45}\)

Vậy \(S=\frac{2}{45}\)

Tk nha bn !!

\(\frac{8}{135}\) nhé

mình nhầm , kết quả là \(\frac{2}{45}\)

\(\left(2007-2005\right)+\left(2003-2001\right)+...+\left(7-5\right)+\left(3-1\right)\)

\(=2+2+...+2\)

\(=2.1004=2008\)

\(\dfrac{1}{1.5};\dfrac{1}{5.9};\dfrac{1}{9.13};\dfrac{1}{13.17}\)

\(I=\dfrac{2}{1\times5}+\dfrac{2}{5\times9}+\dfrac{2}{9\times13}+...+\dfrac{2}{181\times185}\)

\(=\dfrac{1}{2}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{181\times185}\right)\)

\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{181}-\dfrac{1}{185}\right)\)

\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{185}\right)=\dfrac{1}{2}\times\dfrac{184}{185}=\dfrac{92}{185}\)

x trong bài là dấu nhân nha, mik viết nhầm

làm bừa thui,ai tích mình mình tích lại

Số số hạng là : 

Có số cặp là :

50 : 2 = 25 ( cặp )

Mỗi cặp có giá trị là :

99 - 97 = 2 

Tổng dãy trên là :

25 x 2 = 50

Đáp số : 50

A = 1.5 + 5.9 + 9.13 + ...+ 41.45

A = \(\dfrac{12}{12}\).(1.5 + 5.9 + 9.13 +...+ 41.45)

A = \(\dfrac{1}{12}\).(1.5.12 + 5.9.12 + 9.13.12 + ... + 41.45.12)

^{A = \(\dfrac{1}{12}\).[1.5.(9 + 3) + 5.9.(13 - 1) + 9.13.(17 - 5) + ... + 41.45.(49 - 37)]} 

^{A = \(\dfrac{1}{12}\)[1.5.9 + 1.5.3 + 5.9.13 - 1.5.9 + 9.13.17 - 5.9.13 +...+41.45.49 - 41.45.37]}

A =\(\dfrac{1}{12}\).[1.5.3  + 41.45.49]

A = \(\dfrac{1}{12}\).[15 + 90405]

A = \(\dfrac{1}{12}\).90420

A = 7535

^.

6666 +8888=

6666 + 8888 = 15554

Chúc các bạn học tốt

a) \(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}=\frac{29}{45}\)

\(\Rightarrow\frac{7}{x}+\left(\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\right)=\frac{29}{45}\)

\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)

\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)

\(\Rightarrow\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)

\(\Rightarrow\frac{7}{x}=\frac{29}{45}-\frac{8}{45}\)

\(\Rightarrow\frac{7}{x}=\frac{7}{15}\)

\(\Rightarrow x=15\)

Vậy x = 15

b) \(\frac{x}{2008}-\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-\left(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\right)=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-\left(\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\right)=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-2.\frac{3}{16}=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)

\(\Rightarrow\frac{x}{2008}=\frac{5}{8}+\frac{3}{8}\)

\(\Rightarrow\frac{x}{2008}=1\)

\(\Rightarrow x=2008\)

Vậy x = 2008

_Chúc bạn học tốt_