100²-99²+98²-97²+.+2²-1² =(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)=100+99+98+97+...+2+1=(100+1)*100/2=5050 (x+1)(x+2)(x+3)(x+4)+1=[(x+1)(x+4)][(x+2)(x+3)]+1=(x^2+5x...