删除项和扰动网格定理及其应用：对于黎曼定积分的定理
Deleting Items and Disturbing Mesh Theorems for Riemann Definite Integral and Their Applications
AI总结：
本文基于黎曼定积分的定义，给出了关于黎曼和的删除项和扰动网格定理，探讨在删除某些项或扰动网格划分后，黎曼和仍能收敛到黎曼定积分的条件，并展示了这些定理在处理函数级数和乘积的复杂极限问题中的应用，进一步证明了黎曼定积分的几何直观比普通曲边梯形面积思维更深刻。
摘要：
基于黎曼定积分的定义，给出了关于黎曼和的删除项和扰动网格定理。在删除某些项或扰动网格划分后，只要满足特定条件，黎曼和的极限仍能收敛到黎曼定积分。这些定理可以处理一类复杂的和与积的级数极限问题，并证明黎曼定积分的几何直观比普通曲边梯形面积的思维更加深刻。
英文摘要：
Based on the definition of Riemann definite integral,deleting items and disturbing mesh theorems on Riemann sums are given. After deleting some items or disturbing the mesh of partition, the limit of Riemann sums still converges to Riemann definite integral under specific conditions. These theorems can deal with a class of complicate limitation of sum and product of series of a function, and demonstrate that the geometric intuition of Riemann definite integral is more profound than ordinary thinking of area of curved trapezoid.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
