\(A=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)
\(A=-\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)
\(A=-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(A=-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)\)
\(A=-\dfrac{3}{20}\)
`A = (-1)/20 + (-1)/30 + (-1)/42 + (-1)/56 + (-1)/72 + (-1)/90`
`=> A = - (1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)`
`A = - (1/(4xx5) + 1/(5xx6)+ 1/(6xx7) + 1/(7xx8) + 1/(8xx9) + 1/(9xx10))`
`A = - (1/4-1/5+1/5-1/6+.......+1/9-1/10)`
`A=-(1/4-1/10)`
`A=-(5/20 - 2/20)`
`A=-(3/20)`
`=> A= (-3)/20`
