I have been trying to use induction to prove that a recurring sequence is monotone, but the problem that I'm having is that no initial values are given. Can someone please give a hint as to how to approach this?
2026-04-08 12:58:26.1775653106
Proving convergence for recurring sequence?
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Even if $a_n$ tend to some limit $l$, the limit must satisfy the recurrence relation, i.e. $$l={l-1\over l+1}$$which leads to $l^2+l=l-1$ with no solutions in real numbers. So, your sequence is divergent.