Question

\(\frac{3^2}{8.11}\) +\(\frac{3^2}{11.14}\)+\(\frac{3^2}{14.17}\)+...+\(\frac{3^2}{197.200}\)

Answer 1

Đặt \(A=\frac{3^2}{8.11}+\frac{3^2}{11.14}+\frac{3^2}{14.17}+...+\frac{3^2}{197.200}\)

\(\Leftrightarrow A=\frac{9}{8.11}+\frac{9}{11.14}+\frac{9}{14.17}+...+\frac{9}{197.200}\)

\(\Leftrightarrow\frac{1}{3}A=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)

​\(\Leftrightarrow\frac{1}{3}A=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{2}{17}+...+\frac{1}{197}-\frac{1}{200}\)​b

\(\Leftrightarrow\frac{1}{3}A=\frac{1}{8}-\frac{1}{200}\)

\(\Leftrightarrow\frac{1}{3}A=\frac{24}{200}\)

\(\Leftrightarrow A=\frac{24}{200}\times3\)

\(\Leftrightarrow A=\frac{72}{200}=\frac{9}{25}\)

Answer 2

Thank

Answer 3

\(=\frac{3.3}{8.11}+\frac{3.3}{11.14}+...+\frac{3.3}{197.200}\)

\(=3(\frac{3}{8.11}+\frac{3}{11.14}+..+\frac{3}{197.200})\)

\(=3(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200})\)

\(=3(\frac{1}{8}-\frac{1}{200})\)

\(=3(\frac{200}{1600}-\frac{8}{1600})\)

\(=3.\frac{192}{1600}\)

\(=\frac{576}{1600}\)

Answer 4

sao ko rút luôn 9 ra ngoài

Answer 5

9/3.(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. 24/200

=72/200=9/25