Calculating the limit of a seres
If the series is geometric, or in the form
it will be convergent if . The sum will be equal to
If the series is not geometric, it may not be possible to calculate it directly. One way to estimate it is to break the sum into two parts.
The first part of the sum can be calculated directly, while the second part can be estimated by using improper integrals.
The larger is, the more accurate the estimation will be.