=1 - (3 - 103) + (5 - 105) - (7 - 107)+...

=1 + 100 - 100 +100 - ...

=1

a)  \(\dfrac{x}{3}=\dfrac{3}{2}\cdot\dfrac{1}{4}\)

    \(\dfrac{x}{3}=\dfrac{3}{8}\)

     \(x=\dfrac{3\cdot3}{8}\)

     \(x=\dfrac{9}{8}\)

b)   \(\dfrac{x}{5}=\dfrac{-1}{3}:\dfrac{7}{2}\)

      \(\dfrac{x}{5}=\dfrac{-1}{3}\cdot\dfrac{2}{7}\)

       \(\dfrac{x}{5}=\dfrac{-2}{21}\)

       \(x=\dfrac{-2\cdot5}{21}\)

       \(x=-\dfrac{10}{21}\)

c)     \(x+\dfrac{2}{3}=\dfrac{4}{3}-\dfrac{1}{6}\)

       \(\dfrac{6x}{6}+\dfrac{2\cdot2}{3\cdot2}=\dfrac{4\cdot2}{3\cdot2}-\dfrac{1}{6}\)

     \(\dfrac{6x}{6}+\dfrac{4}{6}=\dfrac{8}{6}-\dfrac{1}{6}\)

     \(\dfrac{6x+4}{6}=\dfrac{7}{6}\)

      \(\dfrac{6x+4}{6}-\dfrac{7}{6}=0\)

      \(\dfrac{6x+4-7}{6}=0\)

      \(\dfrac{6x-3}{6}=0\)

      \(6x-3=0\)

      \(6x=3\)

       \(x=\dfrac{3}{6}=\dfrac{1}{2}\)