In this paper we generalized the combinatorial formula for k-bonacci numbers where k is a positive integer by using the well-known step problem. We solved this problem using the combinatorial analysis. We established the relationship between the combinatorial analysis and the famous Fibonacci sequences. We extended our analysis to the case of taking 1 or 2 or 3 or 4 up to k steps at a time, which allowed us to derive a combinatorial equivalent of k-bonacci numbers
This paper presents explicitly a survey of uniformly integrable sequences of random variables. We also study extensively several cases and conditions required for uniform integrability, with the establishment of some new conditions needed for the generalization of the earlier results obtained by many scholars and researchers, noting the links between uniform integrability and pointwise convergence of a class of polynomial functions on conditional based.