正项级数比值判别法的极限形式的推广

The Extension of Ratio Test about Convergence of Positive Series

针对比值判别法的极限形limx→∞un+1/un=q=1的不定情形,对比值判别法的极限形式进行推广,通过limx→∞(un/un+1)n=r可判定当比值判别法的极限形式中limx→∞(un+1/un)=q=1时,一些正项级数的敛散性.

The convergence of positive series Σ∞n=1 un is inconclusive, if limx→∞ un＋1/un=q=1. Based on this case, this paper extends ratio test about convergence of positive series, and we can test the convergence of positive series Σ∞n=1 un by applying thelimit form limx→∞ （un/un＋1）^n=r.