Convergence of a sequence is a mathematical concept that refers to the behavior of a sequence of numbers as it approaches a specific value or limit. It means that the terms in the sequence get closer and closer to the specified limit as the sequence progresses.
There are a few different tests that can be used to determine the convergence of a sequence, including the comparison test, the ratio test, and the root test. These tests involve examining the behavior of the terms in the sequence and comparing them to known patterns of convergence.
Convergence and divergence refer to opposite behaviors of a sequence. Convergence means that the terms in the sequence get closer and closer to a specific limit, while divergence means that the terms in the sequence do not approach a specific limit and may instead grow infinitely large or oscillate between different values.
No, a sequence can only converge to one limit. If a sequence has multiple limits, it is considered to be divergent.
Convergence of a sequence has many practical applications in fields such as physics, engineering, and economics. For example, in physics, it can be used to model the behavior of a particle as it approaches a specific state, while in economics, it can be used to predict the behavior of a market as it approaches equilibrium.