Đặt \(A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)

\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)

\(A=\frac{1}{2}-\frac{1}{17}\)

\(A=\frac{15}{34}\)

= \(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)= \(\frac{1}{2}-\frac{1}{17}\)=\(\frac{15}{34}\)

\(\frac{3}{2.5}\)+\(\frac{3}{5.8}\)+\(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+\(\frac{3}{14.17}\)

=\(\frac{1}{2}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{8}\)+......+\(\frac{1}{14}\)-\(\frac{1}{17}\)

=\(\frac{1}{2}\)-\(\frac{1}{17}\)

=\(\frac{15}{34}\)

bn cho mk đi là câu tl sẽ hiện ra

=3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17)

=3(1/2-1/17)

=3x15/34

=45/34

mk nha

\(\frac{3^2}{2.5}+\frac{3^2}{5.8}+\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}\)

=\(3\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)\)

= \(3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)\)

= ​\(3\left(\frac{1}{2}-\frac{1}{17}\right)\)​​

=\(\frac{45}{34}\)

\(3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)\)​

=3(3/2.5+3/5.8+3/8.11+3/11.14+3/14.17)

=3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17)

=3(1/2-1/17)

=45/34

cô Nhung ơi k đúng cho con đi cô pls

a/ Ta có: \(S=1+\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{27}-\frac{1}{30}\right)\)

\(S=1+\left(\frac{1}{2}-\frac{1}{30}\right)\)

\(S=1+\frac{7}{15}\)

\(S=\frac{22}{15}\)

b/ \(S=-4+\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{107}-\frac{1}{110}\right)\)

\(S=-4+\left(1-\frac{1}{110}\right)\)

\(S=-4+\frac{109}{110}\)

\(S=-3\frac{1}{110}\)

\(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{21.24}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{24}\)

\(=\frac{1}{5}-\frac{1}{24}\)

\(=\frac{19}{120}\)

\(a,A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{90}\)

\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)

\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)

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

\(A=3.\frac{9}{10}=\frac{27}{10}\)

\(b,B=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(B.\frac{3}{2}=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)

\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)

\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{17}\)

\(B=\frac{15}{34}:\frac{3}{2}=\frac{5}{17}\)

a) Lấy A chia 3

b) Lấy B nhân 3/2

15544525 nfhg

Ta có : 

\(A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2009.2012}+\frac{3}{2012.2015}\)

\(A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2009}-\frac{1}{2012}+\frac{1}{2012}-\frac{1}{2015}\)

\(A=\frac{1}{5}-\frac{1}{2015}\)

\(A=\frac{402}{2015}\)

Vậy \(A=\frac{402}{2015}\)

Chúc bạn học tốt ~ 

A =  402/2015 

\(A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2012.1015}\)

\(A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{2012}-\frac{1}{2015}\)

\(A=\frac{1}{5}-\frac{1}{2015}\)

\(A=\frac{402}{2015}\)

a) = 2(1-1/2+1/2-1/3+...+1/19-1/20)

    = 2(1-1/20)

    = 2.19/20

    = 19/10

b) = 7(1/2-1/3+1/3-1/4+...+1/6-1/7)

   = 7(1/2 - 1/7)

   = 7.5/14

   = 5/2

c) = 1/2-1/5+1/5-1/8+...+1/14-1/17

   = 1/2 - 1/17

   = 15/34

Chúc bạn học tốt nhé

a)2/1.2+2/2.3+....+2/19.20

=2(1/1.2+1/2.3+....+1/19.20)

=2(1-1/2+1/2-1/3+.....-1/20)

=2(1-1/20)

2(19/20)=38/20=19/10

b)7/2.3+7/3.4+7/4.5+7/5.6+7/6.7

7(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7)

7(1/2-1/3+1/3-1/4+.....-1/7)

7(1/2-1/7)

7(7/14-2/14)=7.5/14=35/14=5/2

c)3/2.5+3/5.8+3/8.11+3/11.14+3/14.17

1/2-1/5+1/5-1/8+......+1/14-1/17

1/2-1/17=17/34-2/34=15/34

Đây là toán lp 6 chứ bn

A = 2/1.2 + 2/2.3 + ...+2/19.20

Áp dụng công thức : n/n.(n+1)=(1/n)-(1/n+1)

Ta có : A= 1/1.2 + 1/2.3+...+1/19.20

           A= 1/1 - 1/2 + 1/2 - 1/3 + ...+ 1/19 - 1/20

           A= 1/1 - 1/20 

           A= 19/20

k cho mk nha bn