Convergence of Parametrized Series

This lecture explores the convergence of a series parameterized by alpha, focusing on finding the values of alpha for convergence. By comparing the series to the zeta function, it is shown that alpha must be strictly positive for convergence. The general term is studied by comparing it to a known series, leading to the conclusion that the two series are of the same nature. By solving an inequality involving alpha, it is determined that the series converges when alpha is positive and less than or equal to 0.5. The lecture concludes with a discussion on finding the roots of a polynomial to determine convergence.