Alex G said:I thought the same, however, as I calculate out different and higher successive numbers for
1 / sqrt(n^3 + 2n), it's always smaller than 1 / n^(3/2) :(
Alex G said:I thought the same, however, as I calculate out different and higher successive numbers for
1 / sqrt(n^3 + 2n), it's always smaller than 1 / n^(3/2) :(
In Calculus 2, Simple Convergence/Divergence refers to the behavior of a series, which is a sum of an infinite sequence of numbers. A series is said to be convergent if the sum of its terms approaches a finite number as the number of terms increases. On the other hand, a series is divergent if the sum of its terms does not approach a finite number.
Simple Convergence/Divergence can be determined using various tests, such as the comparison test, ratio test, and integral test. These tests help determine the behavior of a series and whether it is convergent or divergent.
Simple Convergence/Divergence is important in Calculus 2 as it helps determine the behavior and convergence of a series. This information is crucial in solving various mathematical problems and applications, such as finding areas under curves and calculating probabilities.
No, a series cannot be both convergent and divergent. A series can only have one of these two behaviors. However, there are cases where a series may not be classified as either convergent or divergent, and in such cases, further testing may be required to determine its behavior.
Simple Convergence/Divergence is closely related to other concepts in Calculus 2, such as limits, derivatives, and integrals. These concepts help determine the behavior of a series and can be used to prove the convergence or divergence of a series. Additionally, the techniques used in Simple Convergence/Divergence, such as the comparison and ratio tests, are also used in other areas of Calculus 2, such as infinite series and improper integrals.