通过对一个周期函数进行傅里叶级数展开，得到了偶数阶的调和级数以及交错的奇数阶调和级数求和的递推公式，然后在此基础之上，得到了其他两类调和级数的递推求和公式。%We develop a recursive formula for even order harmonic series and one for alternating odd order harmonic series by an application of Fourier series expansion of a periodic function with the help of mathematical software-Mathematica 7. And then for the other two kinds of harmonic series, we get similar results derived from the previous ones.
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