\(-1+2-3+4-5+6-.......+98-99+100\)
\(=-1+\left(2-3\right)+\left(4-5\right)+\left(6-7\right)+...+\left(98-99\right)+100\)
\(=-1+\left(-1\right)+\left(-1\right)+...+\left(-1\right)+100\)
\(=\left(-1\right)48+100=-48+100=52\)
-1 + 2 - 3 + 4 -5+6-7+...-99+100
= -1 +(2-3) + (4-5) + (6-7) + ...+ (98-99) + 100
= -1 -1-1-1-...-1+100
= -51 + 100 = 49