1-1/2+1/3-1/4+1/5-1/6.=?有无穷项

1-1/2+1/3-1/4+1/5-1/6.=?有无穷项
1-1/2+1/3-1/4+1/5-1/6.=?
有无穷项

1-1/2+1/3-1/4+1/5-1/6.=?有无穷项
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.

用数学归纳法可证1-1/2+1/3-1/4+...+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+...+1/(2n-1)+1/2n
利用对数不等式1/(x+1)