\(A=\dfrac{25}{18\cdot21}+\dfrac{25}{21\cdot24}+\dfrac{25}{24\cdot27}+...+\dfrac{25}{123\cdot126}\)

\(=25\left(\dfrac{1}{18\cdot21}+\dfrac{1}{21\cdot24}+\dfrac{1}{24\cdot27}+...+\dfrac{1}{123\cdot126}\right)\)

\(=\dfrac{25}{3}\left(\dfrac{3}{18\cdot21}+\dfrac{3}{21\cdot24}+\dfrac{3}{24\cdot27}+...+\dfrac{3}{123\cdot126}\right)\)

\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)

\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)\(=\dfrac{25}{3}\cdot\dfrac{1}{21}=\dfrac{25}{63}\)

A= \(\dfrac{25}{18}-\dfrac{25}{21}+\dfrac{25}{21}-\dfrac{25}{24}+...+\dfrac{25}{123}-\dfrac{25}{126}\)

A= \(\dfrac{25}{18}-\dfrac{25}{126}\)

A= \(\dfrac{25}{21}\)

Hoặc ngay dòng 2 bạn làm như thế này cũng được: \(25.\left(\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)

\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)

\(A=\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)

\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)

\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{126}\right)\)

\(A=\frac{5}{3}.\frac{1}{21}\)

\(A=\frac{5}{63}\)

Đề sai. câu đầu phải là \(\dfrac{1}{18.21}\) mới đúng.
Nếu câu đầu là \(\dfrac{1}{18.21}\) thì mik có cách làm sau :
\(\dfrac{1}{18.21}+\dfrac{1}{21.24}+\dfrac{1}{24.27}+...+\dfrac{1}{123.126}\)

= \(\dfrac{1}{3}.\left(\dfrac{3}{18.21}+\dfrac{3}{21.24}+\dfrac{3}{24.27}+...+\dfrac{3}{123.126}\right)\)

= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{27}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)

= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)

= \(\dfrac{1}{3}.\dfrac{1}{21}\)

= \(\dfrac{1}{63}\)

\(D=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)

\(D=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)

\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)

\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)

\(D=\frac{5}{3}.\frac{1}{21}\)

\(\Rightarrow D=\frac{5}{63}\)

\(3D=3\left(\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+...+\frac{5}{123\cdot126}\right)\)

\(=\frac{3\cdot5}{18\cdot21}+...+\frac{3\cdot5}{123\cdot126}\)

\(=5\left(\frac{3}{18\cdot21}+...+\frac{3}{123\cdot126}\right)\)

\(=5\left(\frac{1}{18}-\frac{1}{21}+...+\frac{1}{123}-\frac{1}{126}\right)\)

\(=5\left(\frac{1}{18}-\frac{1}{126}\right)\)

\(=5\left(\frac{7}{126}-\frac{1}{126}\right)\)

\(=5\cdot\frac{6}{126}\)

\(=\frac{30}{126}\)

\(D=\frac{30}{126}\div3=\frac{30}{126}\cdot\frac{1}{3}=\frac{5}{63}\)

                                    \(#Cothanhkhe\)

A= \(\frac{5}{3}\)(\(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...\frac{3}{123.126}\)

A=\(\frac{5}{3}\)(\(\frac{1}{18}-\frac{1}{126}\))

A=\(\frac{5}{3}.\frac{1}{21}\)

A=\(\frac{5}{63}\)

\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{4}{123.126}\)

    \(=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)

     \(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{123}-\frac{1}{126}\right)\)

      \(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)

       \(=\frac{5}{3}.\frac{1}{21}\)

        \(=\frac{5}{63}\)

1,

\(\dfrac{3}{2^2}\cdot\dfrac{8}{3^2}\cdot\dfrac{15}{4^2}...\dfrac{899}{30^2}\\ =\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}....\dfrac{29\cdot31}{30\cdot30}\\ =\left(\dfrac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot....\cdot30}\right)\cdot\left(\dfrac{3\cdot4\cdot5\cdot....\cdot31}{2\cdot3\cdot4.....\cdot30}\right)\\ =\dfrac{1}{30}\cdot\dfrac{31}{2}\\ =\dfrac{31}{60}\)

2,

\(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{37\cdot38\cdot39}\\ =\dfrac{1}{2}\left(\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{37\cdot38\cdot39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+....+\dfrac{1}{37\cdot38}-\dfrac{1}{38\cdot39}\right)\\ =\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{38\cdot39}\right)\\ =\dfrac{1}{4}-\dfrac{1}{3964}\\ =\dfrac{185}{741}\)

3, Làm tương tự, áp dụng ; \(\dfrac{n}{x\left(x+n\right)}=\dfrac{1}{x}-\dfrac{1}{x+n}\)

3/5*A=3/(18*21)+3/(21*24)+3/(24*27)+...+3/(123*126)

=>3/5*A=1/18-1/21+1/21-1/24+1/24-1/27+...+1/123-1/126

=>3/5*A=1/18-1/126

=>3/5*A=1/21

=>A=5/63

A=\(\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+..........+\frac{3}{123.126}\right)\)

A=\(\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+............+\frac{1}{123}-\frac{1}{126}\right)\)

=\(\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)

=\(\frac{5}{3}.\frac{1}{21}\)

=\(\frac{5}{63}\)

\(D=\dfrac{3}{18\cdot21}+\dfrac{3}{21\cdot24}+\dfrac{3}{24\cdot27}+...+\dfrac{3}{123\cdot126}\\ =\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{27}+...+\dfrac{1}{123}-\dfrac{1}{126}\\ =\dfrac{1}{18}-\dfrac{1}{126}\\ =\dfrac{1}{21}\)

tự giải nhé , kcj khó cả , kq là 1/18 nhé

\(\dfrac{5}{12.17}+\dfrac{35}{17.18}-\dfrac{39}{18.21}+\dfrac{30}{21.72}\)

=\(\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}+\dfrac{1}{18}-\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{5.6}{21.12.6}\)

= \(\dfrac{1}{12}-\dfrac{1}{21}+\dfrac{5}{21.12}\)

=\(\dfrac{21}{12.21}-\dfrac{12}{12.21}+\dfrac{5}{21.12}\)

= \(\dfrac{21-12+5}{12.21}\)

=\(\dfrac{14}{252}\)

\(=\dfrac{1}{18}\)