Let $a_1=a\neq1$ and $a_{n+1}=\dfrac{1}{S_n-1}+1$ then find the $\lim_{n\to \infty}a_n=?$
such that :
$$S_n=\sum_{i=1}^n a_i$$
$$a_1=a \\a_2=\dfrac{1}{a-1}+1 \\a_3=2a+\dfrac{1}{a-1}+1 \\ a_4=3a+2+\dfrac{2}{a-1}+\dfrac{a-1}{2a^2-2a+1} $$
now what do I do ?