\(\text{#}HaimeeOkk\)
Sửa đề : \(\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+...+\dfrac{5}{90}+\dfrac{5}{110}\)
\(=5\text{×}\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{90}+\dfrac{1}{110}\right)\)
\(=5\text{×}\left(\dfrac{1}{3\text{×}2}+\dfrac{1}{3\text{×}4}+...+\dfrac{1}{11\text{×}10}\right)\)
\(=5\text{×}\left(\dfrac{1}{2}-\dfrac{1}{11}\right)\)
\(=5\text{×}\dfrac{9}{22}\)
\(=\dfrac{45}{22}\)
\(\dfrac{5}{8}\rightarrow\)\(\dfrac{5}{6}\)
\(\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+...+\dfrac{5}{90}+\dfrac{5}{110}\)
\(=\dfrac{5}{2\times3}+\dfrac{5}{3\times4}+\dfrac{5}{4\times5}+\dfrac{5}{5\times6}+...+\dfrac{5}{9\times10}+\dfrac{5}{10\times11}\)
\(=\dfrac{5\times1}{2\times3}+\dfrac{5\times1}{3\times4}+\dfrac{5\times1}{4\times5}+\dfrac{5\times1}{5\times6}+...+\dfrac{5}{9\times10}+\dfrac{5}{10\times11}\)
\(=5\times\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{9\times10}+\dfrac{1}{10\times11}\right)\)
\(=5\times\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\right)\)
\(=5\times\left(\dfrac{1}{2}-\dfrac{1}{11}\right)\)
\(=5\times\left(\dfrac{11}{22}-\dfrac{2}{22}\right)\)
\(=5\times\dfrac{9}{22}\)
\(=\dfrac{45}{22}\)
