Штучний інтелект

Анотація: In the paper a theorem that connects the geometrical series with the zeta-function and the logarithmic series is proposed. The theorem rearranges the standard series according to a speed of the convergence of the series. The theorem has mainly a theoretical character but it can be used for an estimation of a convergence of series with non-negative terms. The theorem is adopted to improper integrals.

Ключові слова: series, convergence, zeta-function, logarithmic series, comparison tests, integral test

Посилання:

1. Evgrafov M.A. Rjady i integral’nye predstavlenija. Sovremennye problemy matematiki. Fundamental'nyenapravlenija. T. 13. 1986. 260 s.
2. Cinlar E. Vanderbei R.J. Mathematical Methods of Engineering Analysis. 2000. 119 p.