m: \(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)
\(=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\)
\(=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}+\dfrac{2}{10\cdot13}+\dfrac{2}{13\cdot16}+\dfrac{2}{16\cdot19}\)
\(=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}+\dfrac{3}{16\cdot19}\right)\)
\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{16}-\dfrac{1}{19}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{18}{19}=\dfrac{12}{19}\)
e: \(\dfrac{4}{5}+\dfrac{1}{5}\left(x+1\right)=-\dfrac{2}{5}\)
=>\(\dfrac{1}{5}\left(x+1\right)=-\dfrac{2}{5}-\dfrac{4}{5}=-\dfrac{6}{5}\)
=>x+1=-6
=>x=-6-1=-7
g: \(\dfrac{5}{4}-\dfrac{1}{4}:\left(-\dfrac{1}{2}+x\right)=-1\)
=>\(\dfrac{1}{4}:\left(x-\dfrac{1}{2}\right)=\dfrac{5}{4}+1=\dfrac{9}{4}\)
=>\(x-\dfrac{1}{2}=\dfrac{1}{4}:\dfrac{9}{4}=\dfrac{1}{9}\)
=>\(x=\dfrac{1}{9}+\dfrac{1}{2}=\dfrac{11}{18}\)
