If $$\lim_{n\rightarrow \infty}\frac{s_n -1}{s_n +1}=0$$ then we need to prove: $$\lim_{n\rightarrow \infty}s_n=1.$$
Here is my attempt:
If we express $s_n $ in terms of $t_n$ we've
$$s_n =\frac{-(1+t_n)}{t_n-1}.$$
How to proceed further?
2026-04-02 04:32:42.1775104362
If $\frac{s_n -1}{s_n +1}$ converges to $0,$ then $s_n$ converges to $1?$
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From $$s_n = \frac{-(1+t_n)}{(t_n-1)}$$
And $$\lim_{n\rightarrow \infty} t_n =0$$ we get $$\lim_{n\rightarrow \infty} s_n = \lim_{n \rightarrow \infty} \frac{-(1+t_n)}{(t_n-1)}= \frac{-1}{-1}=1$$