Question

Tính :

A = \(\left(\frac{1}{11x13}+\frac{1}{13x15}+\frac{1}{15x17}+......+\frac{1}{19x21}\right)\)

Answer 1

\(A=\frac{1}{11.13}+\frac{1}{13.15}+..+\frac{1}{19.21}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+..+\frac{1}{19}-\frac{1}{21}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{21}\right)\)

Answer 2

\(A=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+...+\frac{1}{19\cdot21}\)

\(2A=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}\)

\(2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)

\(2A=\frac{1}{11}-\frac{1}{21}+0+...+0\)

\(2A=\frac{10}{231}\)

\(A=\frac{5}{231}\)