Answer:
The limit comparison test is a method used in calculus and real analysis to determine whether an infinite series converges or diverges.
The limit comparison test is based on the idea that if two series have the same behavior, meaning they both converge or both diverge, then their terms must be proportional to each other. Specifically, the limit comparison test states that if a given infinite series a_n has positive terms and the limit of the ratio of a_n and some other series b_n exists and is a finite positive number, then the two series have the same behavior.In other words, if the limit of a_n/b_n is a positive number L, then the series a_n converges if and only if the series b_n converges. If the limit of a_n/b_n is zero or infinity, then the series a_n and b_n have different behavior.
The limit comparison test is a useful tool for determining the convergence or divergence of a series that is difficult to evaluate directly. By comparing it with a known series that has a similar behavior, we can gain insight into whether the series converges or diverges.