一类和式极限的求解

A New Method of Solving a Kind of Sum Limit

本文研究了f(k,n)具有单调性时和式极限lim from (k→+∞) sum from k=1 to n (f(k,n))的求解问题,同时利用无穷小的替换方法,使得其求解过程简单化,然后把这一种方法进一步推广到积式极限的求解。

A question of solving the sum limit of lim ∑n→＋∞ k=1^ n f（k,n））is researched in the case of monotonicity of in the paper. A new method is given, at the same time the process of solving the question is simplified with the replace of the equivalent infinitesimal quantity. Finally, the method is extended further to solve the limitment of a kind of product formula in the paper.