I am doing a sequences homework, and tried solving some given recurrence relations (even though it was not asked). To my surprise, this proved really hard for some relations. For example: $$u_{n+1}=u_n+2\ln(u_n)$$ or an even simpler one, $$u_{n+1}=au_n(1-u_n).$$ Is there a general theorem out there that can help me solve recurrence relations containing only elementary functions?
2026-04-24 22:48:28.1777070908
Is it possible to solve any given recurrence relation?
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No, there is no such general result. You cannot get closed form solutions to recurrence relations (difference equations) any more than you can get closed form solutions to wide classes of differential equations.