Question

Suppose limn→∞ (Sn − 1)/ (Sn + 1) = 0. Prove that limn→∞ Sn = 1.

Answer 1

Given that $lim_{n \to \infty} \frac {S_n-1}{S_n+1}=0$

$\implies \frac {lim_{n \to \infty} (S_n-1)}{lim_{n \to \infty}( S_n+1)}=0$ ........(1)

Now from (1) we can say that as the exists , therefore $lim_{n \to \infty}( S_n+1) \neq 0$

So the only possibility is that , $lim_{n \to \infty} (S_n-1)=0$

$\implies lim_{n \to \infty} S_n=1$

Which completes the proof.