Question

thực hiện phép tính:  2(1/1x3 + 1/3x5 + 1/5x7 + .... +1/13x15)

Answer 1

\(2\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{13.15}\right)=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{13.15}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}=1-\frac{1}{15}=\frac{14}{15}\)

Answer 2

\(=2.2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(=4.\left(1-\frac{1}{15}\right)\)

\(=4.\frac{14}{15}\)

\(=\frac{56}{15}\)