\(1+\left(-2\right)+3+\left(-4\right)+5+...+\left(-98\right)+99\)
\(=\left(1+3+5+...+99\right)+\left[\left(-2\right)+\left(-4\right)+...+\left(-98\right)\right]\)
\(=\frac{100.50}{2}+\frac{-100.49}{2}\)
\(=2500+\left(-2450\right)\)
\(=50\)
\(1+\left(-2\right)+3+\left(-4\right)+...+\left(-98\right)+99\)
\(=\left(1+3+...+99\right)+\left[\left(-2\right)+\left(-4\right)+...+\left(-98\right)\right]\)
\(=\frac{\left(99+1\right).50}{2}+\frac{\left[\left(-98\right)+\left(-2\right)\right].50}{2}\)
\(=2550+\left(-2450\right)=50\)