A limit of a converging sequence is a specific value that the terms of the sequence approach as the index increases towards infinity. In other words, it is the value that the sequence "converges" to.
The limit of a converging sequence can be determined by observing the pattern of the terms in the sequence and using mathematical tools such as the limit laws, the squeeze theorem, or the ratio test.
If a converging sequence does not have a limit, it is considered to be a diverging sequence. This means that the terms in the sequence do not approach a specific value as the index increases towards infinity.
No, a converging sequence can only have one limit. This is because the limit of a sequence is a unique value that the terms in the sequence approach.
The concept of a limit of a converging sequence is used in many areas of science and mathematics, such as in physics, engineering, and economics. It can help determine the behavior of a system or model as it approaches a particular value, and can also be used to make predictions and solve problems.