\(\frac{1}{3}+\frac{1}{6}+...+\frac{2}{x\left(x+1\right)}=\frac{2003}{2009}\)

\(\Rightarrow\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{2003}{2009}\)

\(\Rightarrow2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2003}{2009}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2003}{2009}\)

\(\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2003}{2009}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2003}{2009}\div2\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2003}{4018}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2003}{4018}\)

\(\Rightarrow\frac{1}{x+1}=\frac{3}{2009}\)

\(\Rightarrow\frac{3}{3\left(x+1\right)}=\frac{3}{2009}\)

\(\Rightarrow3\left(x+1\right)=2009\)

\(\Rightarrow3x+3=2009\)

\(\Rightarrow3x=2006\)

\(\Rightarrow x=\frac{2006}{3}\)

Bài dễ tự làm đi

Đặt \(A=\frac{3}{10.12}+\frac{3}{12.14}+.....+\frac{3}{48.50}\)

      \(A=\frac{3}{2}.\left(\frac{2}{10.12}+\frac{2}{12.14}+......+\frac{2}{48.50}\right)\)

      \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+....+\frac{1}{48}-\frac{1}{50}\right)\)

       \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{50}\right)\)

      \(A=\frac{3}{2}.\frac{2}{25}\) 

     \(A=\frac{3}{25}\)

cảm ơn bạn nhiều nhé !
 

a,Góc xÔy => xÔy đối đỉnh x'Ôy' <=> xÔy = x'Ôy' = 100o
Ta có xÔy + yÔx' = xÔx' (kề bù)
100o + yÔx' = 180o
yÔx' = 180o - 100o
yÔx' = 80o
=> yÔx' đối đỉnh xÔy' <=> yÔx' = xÔy' = 80o

Dm may giup tao vay a

gfggd

ta có: \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}+\frac{1}{20}\)( Có 10 phân số 1/20)

                                                                                            \(=\frac{10}{20}=\frac{1}{2}\)

\(\Rightarrow A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}>\frac{1}{2}\)

Chúc bn học tốt !!!!

cảm ơn

a) \(\frac{27}{8}\times\frac{5}{7}\times\frac{8}{27}+\frac{2}{7}\)

\(=\frac{27\times5\times8}{8\times7\times27}+\frac{2}{7}\)

\(=\frac{5}{7}+\frac{2}{7}\)

\(=1\)

b) \(1,6\times\frac{25}{32}-\left(\frac{2}{3}+\frac{4}{5}\right):\frac{11}{5}\)

\(=\frac{8}{5}\times\frac{25}{32}-\left(\frac{2}{3}+\frac{4}{5}\right).\frac{5}{11}\)

\(=\frac{5}{4}-(\frac{10}{33}+\frac{4}{11})\)

\(=\frac{5}{4}-\frac{2}{3}\)

\(=\frac{7}{12}\)

chịu luôn rùi! !   phần b, mk ko tính nhanh đc! cho mk xin lỗi bn nhiều nha!