\(P=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{29.31}\)
=> \(2P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{29.31}\)
\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{31-29}{29.31}\)
\(=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{29}-\frac{1}{31}\right)\)
\(=1-\frac{1}{31}=\frac{30}{31}\)
=> \(P=\frac{30}{31}:2=\frac{15}{31}\)
Nếu đề là tính thì bạn làm như sau nhé :
\(P=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{29.31}\)
\(\Rightarrow2P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{29.31}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{29}-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{30}{31}\)
\(\Rightarrow P=\frac{30}{31}\div2=\frac{15}{31}\)
\(P=\left(\frac{2}{1\cdot3}+\frac{2}{3.5}+\frac{2}{5\cdot7}+...+\frac{2}{29\cdot31}\right)\cdot\frac{1}{2}\)
\(P=\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{29}-\frac{1}{31}\right)\cdot\frac{1}{2}\)
\(P=\left(1-\frac{1}{31}\right)\cdot\frac{1}{2}\)
\(P=\frac{30}{31}\cdot\frac{1}{2}\)
\(P=\frac{15}{31}\)
\(P=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{29\cdot31}\)
\(P=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{29}-\frac{1}{31}\right)\)
\(P=\frac{1}{2}\left(1-\frac{1}{31}\right)=\frac{1}{2}\cdot\frac{30}{31}=\frac{1}{1}\cdot\frac{15}{31}=\frac{15}{31}\)
Ta có : P = 1/1×3 + 1/3×5 + 1/5×7 + .......+ 1/29×31
P= 1/2 ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ......+ 1/29 - 1/31 )
P = 1/2 ( 1 - 1/31 )
P = 1/2 × 30/31
P = 15/31
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