)lha08 said:
The integral test is a method used to determine the convergence or divergence of a series by comparing it to an integral. It states that if the integral of the series is convergent, then the series itself is also convergent. Conversely, if the integral is divergent, then the series is also divergent.
To use the integral test, you must first take the integral of the series. Then, evaluate the integral to see if it is convergent or divergent. If the integral is convergent, then the series is also convergent. If the integral is divergent, then the series is also divergent.
The integral test can only be used for series with positive terms that decrease monotonically (i.e. always decreasing or always increasing). Additionally, the integral must be able to be evaluated using standard integration techniques.
Yes, the integral test can be used to determine both absolute and conditional convergence. If the integral of the series is convergent, then the series is absolutely convergent. However, if the integral is convergent but the series is not, then the series is conditionally convergent.
The integral test can only be used for series with positive terms that decrease monotonically. It also cannot be used for series with alternating signs or series with terms that do not decrease monotonically. Additionally, the integral must be able to be evaluated using standard integration techniques.