- let

- then we can express the ratio

- where we have denoted

- the idea is to try to express the sum as
- where is a polynomial in ;
note that
- substituting (2.1) into (2.2), we obtain a recurrence
relation for :
- to solve the recurrence relation, we need to know the degree of the
polynomial
- we can rewrite (2.3) as
- introducing

and substituting this formula into (2.4), we obtain

- from which it follows that (if , then the previous equation implies that )
- therefore, is a polynomial of at most degree two

- the solution of (2.3) is then

where is an arbitrary real parameter - the value of is obtained from the initial
condition , which gives and
hence,

- the final solution is

Richard Liska