lim n→∞ sum n^kf[i^q/n^p] from i=1 to n型极限的计算公式及其应用

The Formula on Limitation of lim n→∞ sum n^kf[i^q/n^p] from i=1 to n Type and Its Application

对p>q≥0情形下,形如lim n→∞ sum n^kf[i^q/n^p] from i=1 to n的一类和式极限,给出并证明了其计算公式。该公式在求解这类极限时具有计算简便、适用面宽等优点,进一步还可运用于可化为这类和式极限的积式极限的计算。

Under the circumstances of p q ≥ 0, the finite sums limit is shaped like lim n→∞ sum n∑i=1 n^kf[i^q/n^p] this paper presents and proves its formula. This formula has the advantages of simple calculation with wide applicability and can also be applied to the calculations of this product type limit.