Convergence refers to a sequence or series of numbers that approaches a specific limit or value as the number of terms increases. Divergence, on the other hand, refers to a sequence or series of numbers that does not approach a specific limit and instead grows towards infinity.
2.There are various tests that can be used to determine convergence or divergence, such as the ratio test, the root test, and the comparison test. These tests involve analyzing the behavior of the terms in a series and determining if they approach a limit, grow towards infinity, or alternate between positive and negative values.
3.Determining convergence or divergence is important in mathematics and science because it allows us to understand the behavior of a sequence or series of numbers. It also helps us to determine the accuracy and validity of mathematical models and predictions.
4.If a series is neither convergent nor divergent, it is said to be indeterminate. This means that further analysis and tests are needed to determine the behavior of the series. In some cases, a series may oscillate between converging and diverging, making it difficult to determine its behavior.
5.No, a series can either converge or diverge, but not both simultaneously. It is possible for different parts of a series to converge or diverge, but the overall behavior must be either convergent or divergent.