1/5*7 + 1/7*9 + 1/9*11 + ... + 1/13*15
= 1/2(2/5*7 + 2/7*9 + 2/9*11 + ... + 2/13*15)
= 1/2(1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15)
= 1/2(1/5 - 1/15)
= 1/2.2/15
= 1/15
Bài giải
\(\text{Đặt }A=\frac{1}{5\text{ x }7}+\frac{1}{7\text{ x }9}+\frac{1}{9\text{ x }11}+\frac{1}{11\text{ x }13}+\frac{1}{13\text{ x }15}\)
\(A=\frac{1}{2}\left(\frac{2}{5\text{ x }7}+\frac{2}{7\text{ x }9}+\frac{2}{9\text{ x }11}+\frac{2}{11\text{ x }13}+\frac{2}{13\text{ x }15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{15}\)
\(A=\frac{1}{15}\)
Bài giải
\(\text{Đặt }A=\frac{1}{5\text{ x }7}+\frac{1}{7\text{ x }9}+\frac{1}{9\text{ x }11}+\frac{1}{11\text{ x }13}+\frac{1}{13\text{ x }15}\)
\(A=\frac{1}{2}\left(\frac{2}{5\text{ x }7}+\frac{2}{7\text{ x }9}+\frac{2}{9\text{ x }11}+\frac{2}{11\text{ x }13}+\frac{2}{13\text{ x }15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{15}\)
\(A=\frac{1}{15}\)
Đặt A = \(\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+\frac{1}{11\times13}+\frac{1}{13\times15}\)
A = \(\frac{1}{2}\left(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}+\frac{2}{13\times15}\right)\)
A = \(\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
A = \(\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)
A = \(\frac{1}{2}.\frac{2}{15}\)
\(A=\frac{1}{15}\)
Đặt \(D=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(\Leftrightarrow D=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(\Leftrightarrow D=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(\Leftrightarrow D=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{15}\right)\)
\(\Leftrightarrow D=\frac{1}{2}.\frac{2}{15}=\frac{2}{30}=\frac{1}{15}\)
~ Hok tốt ~
