a: \(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{-37}{45}\)
=>\(x+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{-37}{45}\)
=>\(x+\dfrac{9}{45}-\dfrac{1}{45}=\dfrac{-37}{45}\)
=>x=-1
b: \(\Leftrightarrow x-10\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)
\(\Leftrightarrow x-10\cdot\dfrac{4}{55}=\dfrac{3}{11}\)
=>\(x-\dfrac{4}{11}=\dfrac{3}{11}\)
=>x=7/11
c: \(\Leftrightarrow2\left(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2}{9}\)
=>\(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{9}\)
=>1/x+1=1/6-1/9=1/18
=>x+1=18
=>x=17
