1: \(=\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{-2}{3}+\dfrac{2}{3}\right)+\left(\dfrac{3}{4}-\dfrac{3}{4}\right)+\left(\dfrac{-4}{5}+\dfrac{4}{5}\right)+\left(\dfrac{5}{6}-\dfrac{5}{6}\right)+\left(\dfrac{-6}{7}+\dfrac{6}{7}\right)+\left(\dfrac{7}{8}\right)+1\)
=7/8+1
=15/8
2: \(P=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)
\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
=2/99-1=-97/99
3: \(=\left(\dfrac{-3}{4}-\dfrac{2}{9}-\dfrac{1}{36}\right)+\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)+\dfrac{1}{64}\)
\(=\dfrac{-27-8-1}{36}+\dfrac{5+9+1}{15}+\dfrac{1}{64}\)
=1/64