The **limit of a series** is the value a series approaches as the number of terms approaches infinity. If the limit is infinite, the series is divergent. If it is finite, it is called convergent.

## 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

For example,

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.