Answer to Question #155549 in Real Analysis for Gaurav Dabas

Question

if a sequence ⟨Sn⟩ is defined by Sn = Sn/1-Sn-1, s>0, s1>0. then show that the sequence converges to the positive root of the equation x²+x-5=0

Answer 1

* I think the question is wrong. The given sequence is not defined properly.

If $S_n=\frac {S_n}{1-S_{n-1}}$ , then it gives $S_{n-1}=0$ , which contradict $S_1>0$ .

Also here $s>0$ ,which is not defined.