$$\frac{1}{2}~ (19 \times 18-18 \times 17+17 \times 16-16 \times 15+\cdots$$$$ +5\times4-4\times3 +3\times2-2\times1 )$$． 
Overseas Competition->Knowledge Point->Calculation Modules->Fractions
$$\dfrac{1}{2}(19\times18-18\times17+17\times16-16\times15+\cdots$$$$+5\times4-4\times3+3\times2-2\times1)$$  $$=\dfrac{1}{2} (2(18) + 2(16) + \cdots + 2(2))$$  $$= 18 + 16 + 14 +\cdots + 2$$  $$= 2(1 + 2 + \cdots + 9)$$  $$= 2(45)$$  $$= 90$$ 