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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                                    \(#Cothanhkhe\)

Bạn trên làm sai rồi

D=5/18.21+5/21.24+…+5/123.126

D.3/5=3/5.(5/18.21+5/21.24+…+5/123.126

D.3/5=3/18.21+3/21.24+…+3/123.126

D.3/5=(1/18-1/21)+(1/21-1/24)+…+(1/123-1/126)

D.3/5=1/18-1/21+1/21-1/24+…+1/123-1/126

D.3/5=1/18-(1/21-1/21)+…+(1/123-1/123)-1/126

D.3/5=1/18+0+0+…+0-1/126

D.3/5=1/18-1/126

D.3/5=7/126-1/126

D.3/5=5/126

D=5/126:3/5

D=5/126.5/3

D=25/378

Vậy D=25/378

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

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

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

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

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

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

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

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

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

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

. Tham khảo nha bạn: https://olm.vn/hoi-dap/question/894463.html

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

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

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

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

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

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

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 = 54/15.18   +   54/18.21  +  .........+   54/87.90

A = 54/3 . ( 1/15.18 + 1/18.21 + ........+ 1/87.90)

A = 54/3 . ( 1/15 - 1/18 + 1/18 -1/21 + ......+ 1/87 - 1/90)

A =54/3 . ( 1/15 -1/90)

A = 54/3 . 1/18 = 1

vậy A = 1

D=\(\frac{6}{15.18}\)+\(\frac{6}{18.21}\)+...+\(\frac{6}{87.90}\)

D=2.\(\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

D=2.\(\frac{1}{18}\)

D=\(\frac{1}{9}\)

Vậy D=\(^{\frac{1}{9}}\)

\(D=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)

\(D=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)

\(D=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(D=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(D=2.\left(\frac{6}{90}-\frac{1}{90}\right)\)

\(D=2.\frac{1}{18}\)

\(D=\frac{1}{9}\)

a/

\(1995^n.1997^n=\left(1995.1997\right)^n\)

\(1996^{2n}=\left(1996^2\right)^n\)

\(1995.1997=\left(1996-1\right).\left(1996+1\right)=1996^2-1\)

\(\Rightarrow1995.1997< 1996^2\Rightarrow1995^n.1997^n< 1996^{2n}\)

b/

\(A=\frac{1}{2.9}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{9.20}+\frac{1}{9.30}+\frac{1}{9.42}+\frac{1}{9.56}\)

\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)

\(A=\frac{1}{9}\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{8-7}{7.8}\right)\)

\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)\)

\(A=\frac{1}{9}\left(1-\frac{1}{9}\right)=\frac{1}{9}.\frac{8}{9}=\frac{8}{81}\)