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3602x27-9060:453
=97254-9060:453
=97254-20
=9734
CHÚC BẠN HỌC TỐT
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
\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{27}{480}\)
\(=\frac{1}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{27}{480}\)
\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{27}{480}\)
\(=\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{27}{480}\)
\(=\frac{1}{5}-\frac{1}{x+3}=\frac{27}{480}.3\)
\(=\frac{1}{5}-\frac{1}{x+3}=\frac{81}{480}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{81}{480}=\frac{15}{480}=\frac{1}{32}\)
\(\Rightarrow x+3=32\)
\(\Rightarrow x=32-3=29\)
\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{27}{480}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{27}{480}.\frac{1}{3}\)
\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{3}{160}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{1}{160}\)
\(\Rightarrow\frac{1}{x+3}=\frac{31}{160}\)
\(\Rightarrow160=31x+93\)
\(\Rightarrow31x=67\)
\(\Rightarrow x=\frac{67}{31}\)
