a) $\frac{84×143-42×286}{1+2+...+100}=$ $\frac{2×42×143-42×2×143}{1+2+...+100}=$ $\frac{0}{1+2+...+100}=0$
b) 1/(10×11)+1/(11×12)+1/(12×13)+...+1/(99×100)
= 1/10-1/11+1/11-1/12+1/12+1/13+...+1/99-1/100
= 1/10-1/100=9/100
c) 2/(1×2)+2/(2×3)+2/(3×4)+...+2/(2019×2020)
= 2×[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2019×2020)]
= 2×(1-1/2+1/2-1/3+1/3-1/4+...+1/2019-1/2020)
= 2×(1-1/2020)
= 2×2019/2020=2019/1010
d) 1/2+1/6+1/12+1/20+...+1/930
= 1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+...+1/(30×31)
= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/30-1/31
= 1-1/31=30/31