用裂项相消 (1)=1/(1*2)+1/(2*3)+1/(3*4)+…+1/(9*10)=1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10=1-1/10=9/10 (2)=1/3*(1-1/4+1/4-1/7…+1/13-1/16)=5/16 裂项相消用于类似1/ab+1/(b*(b+(b-a)…(的情况)=1/(b-a)*(1/a-1/b...