Question

2/2x5 + 2/5x8 + 2/8x11 + 2/11x14

Answer 1

`2/(2xx5)+2/(5xx8)+2/(8xx11)+2/(11xx14)`

`=2/3.(3/(2xx5) + 3/(5xx8) + 3/(8xx11) + 3/(11xx14)`

`=2/3.(1/(2xx5) + 1/(5xx8) + 1/(8xx11) + 1/(11xx14)`

`=2/3 . (1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14)`

`=2/3.(1/2-1/14)`

`=2/3. 3/7`

`=(2xx3)/(3xx7)`

`=2/7`

Answer 2

\(=\dfrac{2}{3}\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}\right)\)

\(=\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\right)\)

\(=\dfrac{2}{3}\cdot\dfrac{6}{14}=\dfrac{2}{3}\cdot\dfrac{3}{7}=\dfrac{2}{7}\)