Question

\(\dfrac{1}{2}\) + \(^{\dfrac{1}{6}}\)+ \(\dfrac{1}{12}\)+\(^{\dfrac{1}{20}}\)+ \(\dfrac{1}{30}\)+ \(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)

Answer 1

\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{7\cdot8}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\\ =\dfrac{1}{1}-\dfrac{1}{8}\\ =\dfrac{7}{8}\)

Answer 2

`1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56`

`=1/(1xx2) + 1/(2xx3) +1/(3xx4) + 1/(4xx5) + 1/(5xx6) +1/(6xx7) + 1/(7xx8)`

` =1 - 1/2 + 1/2 - 1/3 + ..... + 1/8`

` = 1 - 1/8`

` = 8/8 -1/8`

` = 7/8`

Answer 3

`1/2+1/6+1/12+1/20+1/30+1/42+1/56`

`=`\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\)

`=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8`

`=1-1/8=8/8-1/8=7/8`