\(\dfrac{11}{12}+\dfrac{11}{20}+\dfrac{11}{30}+\dfrac{11}{42}+\dfrac{11}{56}+\dfrac{11}{72}\)
\(=11\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)\)
\(=11\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{8.9}\right)\)
\(=11\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
\(=11\left(\dfrac{1}{3}-\dfrac{1}{9}\right)\)
\(=11\left(\dfrac{3}{9}-\dfrac{1}{9}\right)\)
\(=11.\dfrac{2}{9}\)
\(=\dfrac{22}{9}\)
` c/ 11/12 + 11/20 + 11/30 + 11/42 + 11/56 + 11/72 `
` = ( 11/12 + 11/20 + 11/30 ) + (11/42 + 11/56 + 11/72 )`
` = ( 55/60 + 33/60 + 22/60 ) + ( 132/504 + 99/504 + 77/504 ) `
` = 11/6 + 11/18 `
` = 22/9`
\(c.\dfrac{11}{12}+\dfrac{11}{20}+\dfrac{11}{30}+\dfrac{11}{42}+\dfrac{11}{56}+\dfrac{11}{72}\)
\(=11.\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)\)
\(=11.\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\right)\)
\(=11.\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
\(=11.\left(\dfrac{1}{3}-\dfrac{1}{9}\right)\)
\(=11.\dfrac{2}{9}\)
\(=\dfrac{22}{9}\)
