approximating sums of rational functions
Given a sum of the form where is a rational function, it is possible to approximate it by approximating by another rational function which can be summed in closed form. Furthermore, the approximation so obtained becomes better as increases.
We begin with a simple illustrative example. Suppose that we want to sum . We approximate by , which factors as . Then, upon separating the approximate summand into partial fractions, the sum collapses:
Using a similar approach, we may estimate the error of our approximation.
[general method to come]
|Title||approximating sums of rational functions|
|Date of creation||2013-03-22 18:42:23|
|Last modified on||2013-03-22 18:42:23|
|Last modified by||rspuzio (6075)|