Question

1/5.8+1/8.11+1/11.14+...+1/x(x+3)=27/480

Answer 1

Đặt 1/5.8 + 1/8.11 +...+ 1 /x (x+3) = A

3A = 3/5.8 + 3/8.11 +...+ 3/x (x+3)

3A = 1/5 - 1/8 + 1/8 - 1/11 +...+ 1/x - 1/x+3

3A = 1/5 - 1/x + 3 

3A = ( 3+x)-5/5x +15

A =[ ( 3+ x ) - 5 / 5x + 15 ] : 3

A = x + ( - 2 ) / 5x + 15

   Ta có :

A + 27/480

= x + ( - 2 ) / 5x + 15

=> x + ( - 2 ) = 27

=> 5x + 15 = 480

          * Làm nốt *

                #Louis

Answer 2

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{27}{480}\)

\(=\frac{1}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{27}{480}\)

\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{27}{480}\)

\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{27}{480}\)

\(=\frac{1}{5}-\frac{1}{x+3}=\frac{27}{480}.3\)

\(=\frac{1}{5}-\frac{1}{x+3}=\frac{81}{480}\)

\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{81}{480}=\frac{15}{480}=\frac{1}{32}\)

\(\Rightarrow x+3=32\)

\(\Rightarrow x=32-3=29\)

Answer 3

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{27}{480}\)

\(\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{27}{480}\)

\(\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{27}{480}:\frac{1}{3}\)

\(\frac{1}{5}-\frac{1}{x+3}=\frac{27}{160}\)