IF the limit exists, then take the limit of both sides of the recursion equation: . If the limit exists and , then both of those limits are a. You get the equation . Solve that equation for a.

Of course, that only worksifthe sequence converges. Here you can see that the first few numbers are 1, 3/2, 7/4, .... You should be able to prove, by induction, that this sequence is increasing and has 2 as an upper bound. By the "monotone sequence theorem", then, the sequence converges.