本题精确值很难求出,可以通过下面方法求其近试值:2×1/3+3×1/4+4×1/5+.+99×1/100 =(1-1/2)+(1-1/3)+(1-1/4)+(1-1/5)+.+(1-1/100)-1/2 =98.5-(1/2+1/3+1/4+1/5+.+1/100) ≈98.5-(c-1+㏑100) ≈98.5-0.577215+1-4.60517 =94.317615 ≈94.3 注:式中c是欧拉常数:c=0.577215.