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