1 | initial version |

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`

.

2 | No.2 Revision |

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.

3 | No.3 Revision |

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).

4 | No.4 Revision |

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.

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