Question

2/5*7 2/7*9 2/9*11 ... 2/13*15

Answer 1

`2/(5 xx 7) xx 2/(7xx9) xx 2/(9xx11) xx ... xx 2/(13 xx 15)`

`=1/5-1/7+1/7-1/9+1/9-1/11+....+1/13-1/15`

`=1/5-1/15`

`=3/15-1/15`

`=2/15`

Answer 2

Ta có: \(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+...+\dfrac{2}{13\cdot15}\)

\(=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}\)

\(=\dfrac{1}{5}-\dfrac{1}{15}=\dfrac{2}{15}\)