调和级数与P级数sum from n=1 to ∞(1/n^p)敛散性简证

Proof of Convergence and Divergence of Harmonic Series and P Series

传统教科书在讨论调和级数与p-级数敛散性时非常注重知识的衔接,完整严谨地证明了p级数与调和级数的敛散性。在实践中,学生是学习和研究数学的主体。面对不同的教学对象,对教材及内容的讨论应当适度灵活。本文将用几种简明证法讨论调和级数和p-级数敛散性,以供比对和参考。

Traditional textbooks emphasize the connection of interrelated knowledge on the con vergence and divergence of harmonic series and P series, and have proved it completely and rigor- ously. In practice, the students are the main body of mathematics study and research. Facing dif ferent teaching objects, teachers should be flexible with the discussion of textbook contents. Therefore, several simple proofs are proposed to discuss the convergence and divergence of har monie series and P series so as to provide comparison and reference.