lanedance said:have you heard of stirlings approximation?
The "mystery" behind convergence refers to the mathematical problem of determining whether a series, such as the one given in the question, will approach a finite value (converge) or diverge (approach infinity) as more terms are added.
The notation \sum_{k=2}^{\infy}(\frac{1}{ln(k!)}) represents a series in which the terms are added from k=2 to infinity. The term being added is the reciprocal of the natural logarithm of k factorial.
The "k!" in the series represents the factorial function, which is the product of all positive integers from 1 to k. In this series, the factorial is being used to determine the number of terms in the series, as k increases.
The convergence of this series can be determined using various mathematical tests, such as the ratio test or the integral test. These tests involve comparing the given series to a known convergent or divergent series.
Understanding convergence is important in various fields, such as physics, engineering, and finance. It can be used to model and predict the behavior of systems, such as population growth or stock prices. Additionally, it is essential for ensuring the accuracy and stability of numerical methods in computing and data analysis.