Application of Infinitesimal in Limit and Positive Series
Ling Shou-quan · Journal of Hebei North University · 2008
The limit operation on sum-difference with infinitesimal,based on equivalent infinitesimal replacement,is discussed.And sufficient conditions for equivalent replacement in the limit operation on sum-difference with infinitesimal of same or not same order are given.The structure of product-quotient with equivalent infinitesimal replacement is extended to sum-difference,thus calculation process of limit may be greatly simplified,enabling us aware of when to use equivalent replacement and when to omit it while calculating sum-difference limit.And application of the two theorems in limit calculation.This is illustrated with examples.Meanwhile,the limit form of discriminance about convergence and divergence of positive series compared with infinitesimal are explained.Its application of infinitesimal is explained,and it is of much help for us to understand the discriminance clearly.