Question

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A = \(\frac{4}{1\cdot3}+\frac{4}{3\cdot5}+\frac{4}{5\cdot7}+...+\frac{4}{11\cdot13}\)


 

Answer 1

A=\(2.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\right)\)

A=\(2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)

A=\(2.\left(1-\frac{1}{13}\right)\)

A=\(2.\frac{12}{13}=\frac{24}{13}\)

Answer 2

A=2(2/1.3+2/3.5+2/5.7+...+2/11.13)

A=2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/11-1/13)

A=2(1/1-1/13)=2.12/13=24/13

Answer 3

Ta có:

\(A=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{11.13}\)

\(A=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\right)\)

\(A=2\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(A=2\left(\frac{1}{1}-\frac{1}{13}\right)\)

\(A=2.\frac{12}{13}\)

\(A=\frac{24}{13}\)