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The simple reason is that your conjecture is False. Try with:

A = 1
b = 2
c = 1/2

You will get :

sage: Sequence_rec(3) - Sequence_rec(2)
-20/3

Note also that the denominator can vanish along the loop when i=c+2.

The simple reason is that your conjecture is False. Try with:

A = 1
b = 2
c = 1/2

You All those numbers are strictly positive, but you will get : get:

sage: Sequence_rec(3) - Sequence_rec(2)
-20/3

Note also that the denominator can vanish along the loop when i=c+2., which may be another cause of trouble.

The simple reason is that your conjecture is False. Try with:

A = 1
b = 2
c = 1/2

All those numbers are strictly positive, but you will get:

sage: Sequence_rec(3) - Sequence_rec(2)
-20/3

Note also that the denominator can vanish along the loop when i=c+2, which may be another cause of trouble.trouble (you will have a lot of poles). By the way, even if the sequence was indeed increasing, Sage will not be able to give an answer for all n together (it does not understands loops symbolically, and you could even imagine coding undecidable problems there).

The simple reason is that your conjecture is False. Try with:

A = 1
b = 2
c = 1/2

All those numbers are strictly positive, but you will get:

sage: Sequence_rec(3) - Sequence_rec(2)
-20/3

Note also that the denominator can vanish along the loop when i=c+2, which may be another cause of trouble (you will have a lot of poles). By the way, even if the sequence was indeed increasing, Sage will not be able to give an answer for all n together (it does not understands loops symbolically, and symbolically). Moreover, you could even imagine coding to encode undecidable problems there).in the iteration of such formulas.