The series convergence problem presented involves the infinite series $\sum^{n=0}_{\infty}\frac{2n-1}{\sqrt{n^{5}+1}}$. The solution was reached by analyzing the behavior of the terms as \( n \) approaches infinity. The series converges due to the dominant term in the denominator, which grows faster than the numerator, leading to a limit of zero for the terms of the series.
PREREQUISITESStudents and educators in mathematics, particularly those focused on calculus and series analysis, as well as anyone seeking to deepen their understanding of convergence in infinite series.