设A=48×（1/3-4+1/4－4+…1/100－4）,那么与A最接近的正整数是

A=48[1/(1*5)+1/(2*6)+1/(3*7)+1/(4*8)+1/(5*9)+...+1/(94*98)+1/(95*99)+1/(96*100)+1/(97*101)+1/(98*102)] 因为1/(1*5)=1/4(1/1-1/5) 1/(2*6)=1/4(1/2-1/6) 所以上式可转化为 A=48*1/4*(1-1/5+1/2-1/6+1/3-1/7+1/4-1/8+1/5-1/9+...+1/94-1/98+1/95-1/99+1/96-1/100+1/97-1/101+1/98-1/102) =12(1+1/2+1/3+1/4-1/99-1/100-1/101-1/102) =25-12(1/99+1/100+1/101+1/102) 约=24.52 所以A最接近正整数25