The sequence is the solution of the difference equation...

(1)

... that can be written as...

(2)

As illustrated in...

http://www.mathhelpforum.com/math-he...-i-188482.html

... the solution of (2) is...

(3)

In Your case is and the solution is more clear if we examine two possible alternatives...

a) if we suppose that , then applying (3) we obtain...

(4)

... and the series in (4) converges...

b) if we suppose that , then is...

(5)

Kind regards