Cauchy's Rule

This lecture covers Cauchy's rule for series convergence, which states that if the limit of the nth root of the absolute value of the series terms is less than 1, then the series converges absolutely. The proof involves finding a suitable N such that the terms are bounded by a geometric sequence. Conversely, if the limit is greater than 1, the series diverges. The rule is inconclusive when the limit equals 1. An example is provided to illustrate the application of the rule.