\(B=\frac{9}{8\cdot11}+\frac{9}{11\cdot14}+...+\frac{9}{197\cdot200}\)
\(=3\left(\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{197\cdot200}\right)\)
\(=3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)
\(=3\left(\frac{1}{8}-\frac{1}{200}\right)\)
\(=3\left(\frac{24}{200}-\frac{1}{200}\right)\)
\(=3\cdot\frac{23}{200}\)
đúng
\(\Rightarrow B=3\left(\frac{3}{8.11}\right)+3\left(\frac{3}{11.14}\right)+..+3\left(\frac{3}{197.200}\right)\)
\(\Rightarrow B=3\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{197.200}\right)\)
\(\Rightarrow B=3\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)
\(\Rightarrow B=3\left(\frac{1}{8}-\frac{1}{200}\right)=3.\frac{3}{25}=\frac{9}{25}\)
Vậy \(B=\frac{9}{25}\)
Chúc bn học tốt..!
B = 3^2/8.1 + 3^2/11.14 + 3^2/14.17 +...+ 3^2/7.200
= 3.3/8.11 + 3.3/11.14 +...+ 3.3/197.200
= 3.(3/8.11 + 3/11.14 +...+ 3/197.200)
= 3.(1/8 - 1/11 + 1/11 - 1/14 +...+ 1/197 - 1/200)
= 3.(1/8 - 1/200)
= 3. 3/25
= 9/25