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Question: How to get this recursive sequence of A[n] (warning: too many levels of recursion) ?

Question:How to get this recursive sequence of A[n] (warning: too many levels of recursion) ?

Aixleft math 120 Maple 2024
rsolve recurrence
November 26 2024
1

Hi, how to rsolve this recursive sequence auto? 

The manual calculation is taking the reciprocal of both sides of the equation, and then do some simple calculations to get the answer:1/(3·2^n-5).

> 

restart; A := 'A'; A[n] := `assuming`([rsolve({A[1] = 1, A[n+1] = A[n]/(5*A[n]+2)}, A[n])], [n::posint]); A[n] := simplify(%); simplify(subs(n = 1, %))

Error, recursive assignment

  

A

  

Error, (in simplify/table) too many levels of recursion

  

Download ask_recrusive_sequence_of_A[n].mw
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