\(32\left(\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+....+\frac{3}{197.200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\right)-x=\frac{1}{2}\)

\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{200}\right)-x=\frac{1}{2}\)

x=0.78

a) gọi d là UCLN ( n+3 ; 2n+5)

2n+5\(⋮\) d

n+3\(⋮\)d \(\Rightarrow\)2.(n+3) \(⋮\) d

vậy 2n+6 \(⋮\)d

2n+5 \(⋮\)d

=> 2n+6 - ( 2n+5) \(⋮\) d

=> 1\(⋮\) d

=> d =1

vì UCLN của n+3 và 2n+5 là 1 => dpcm

b)

\(A=\dfrac{3^2}{3}.\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+....+\dfrac{1}{1997}-\dfrac{1}{2000}\right)\)

\(A=3.\left(\dfrac{1}{8}-\dfrac{1}{2000}\right)\)

\(A=\dfrac{747}{2000}\)

B dễ quá bạn suy nghĩ cho thông đầu nhé

=3(\(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+...+\(\frac{3}{1997.2000}\))

=3(\(\frac{1}{8}\)-\(\frac{1}{11}\)+\(\frac{1}{11}\)-\(\frac{1}{14}\)+...+\(\frac{1}{1997}\)-\(\frac{1}{2000}\))

=3(\(\frac{1}{8}\)-\(\frac{1}{2000}\))=3.\(\frac{249}{2000}\)=\(\frac{747}{2000}\)

\(A=3.\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{1997.2000}\right)\)

\(=3.\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{1997}-\frac{1}{2000}\right)\)

\(=3.\left(\frac{1}{8}-\frac{1}{2000}\right)\)

\(=3.\frac{249}{2000}\)

\(\frac{747}{2000}\)

A = 3 (3 / 8.11 + 3 / 11.14 + ..... + 3/1997.2000)

A = 3.(1/8 - 1/11 + 1/11 - 1/14 +........+1/1997 - 1/2000)

A = 3.(1/8 - 1/2000)

A = 3 .249/2000

A = 747/2000

Ta có : 

\(x-\left(\frac{3^2}{8.11}+\frac{3^2}{11.14}+...+\frac{3^2}{1997.2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{1997.2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{1997}-\frac{1}{2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3\left(\frac{1}{8}-\frac{1}{2000}\right)=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-3.\frac{249}{2000}=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x-\frac{747}{2000}=\frac{-1}{2}\)

\(\Leftrightarrow\)\(x=\frac{-1}{2}+\frac{747}{2000}\)

\(\Leftrightarrow\)\(x=\frac{-253}{2000}\)

Vậy \(x=\frac{-253}{2000}\)

Chúc bạn học tốt ~ 

cảm ơn nhé

x - 3( \(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+.................+ \(\frac{3}{1997.2000}\)) = \(\frac{-1}{2}\)

x - 3(\(\frac{1}{8}\)-  \(\frac{1}{11}\)+ \(\frac{1}{11}\)- \(\frac{1}{14}\)+..................+ \(\frac{1}{1997}\)- \(\frac{1}{2000}\)) =\(\frac{-1}{2}\)

x  - 3.\(\frac{249}{2000}\)= \(\frac{-1}{2}\)

x -  \(\frac{747}{2000}\)=\(\frac{-1}{2}\)

x                      =\(\frac{-1}{2}+\frac{747}{2000}\)

x                         =\(\frac{-253}{2000}\)

                        Vậy x = \(\frac{-253}{2000}\)

=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14

=1/2-1/14

=7/14-1/14=6/14=3/7

Gọi A=1/5.8+1/8.11+1/11.14+...+1/605.608

A×3=3/5.8+3/8.11+3/11.14+...+3/605.608

A×3=1/5-1/8+1/8-1/11+1/11-1/14+...+1/605-1/608

A×3=1/5-1/608

A×3=603/3040

A=603/3040÷3

A=201/3040

khi ko mún tích thì tích 1 tích

khi mún tích thì tích 50 tích