解：把ln（x+1）按泰勒级数展开得ln（x+1）=x-(1/2)x^2+(1/3)x^3-(1/4)x^4+......取x=1，则1-1/2+1/3-1/4+1/5-1/6.....=ln2
1/(n+1)+1/(n+2)+........+1/2n
