Convergence問題~20分！

Let convergence of {sn} be k
because for n>2, sn = 1 / s(n-1) + s(n-2)
k= 1/k +k, 1/k= 0, which is absurd.

To prove {sn} cannot be convergent to any number k is much simpler.
If it is really convergent, for any arbitary small number e>0,
there exist N for all n>N such that |sn - s(n-2)| < e

However, aware that sn - s(n-2) = 1/s(n-1)
that means for all n>N, s(n-1) > 1/e
Because we pick e so small that 1/e > k (the convergent mentioned above), so convergence is not possible.

2007-01-24 00:33:24 補充：
1) By induction, you can prove {sn} is positive sequence. That may help you to prove the sequence is not convergent to any number.2) I only want to give concept. Above step may be incomplete for homework purpose. For that purpose, you need to do it yourself.