# Compare elements of a recursive defined sequence

I define the recursive sequence as:

```
A, b, c = var('A, b, c')
def Sequence_rec(k):
x = 0
for i in range(1,k+1):
x = x + (A - x)/((c-i+2)^b)
return x
```

For the parameters the assumptions are:

```
assume(A>0,c>0,b>0)
assume(c, 'integer')
```

I'm interested in the elements of Sequence_rec(k) with k<=c. The following relation has to be true for the defined sequence considering the given assumptions:

```
assume(c>2)
bool(Sequence_rec(4) > Sequence_rec(3))
```

But Sage computes it is false! The following plot shows the difference is positive:

```
plot((Sequence_rec(4) - Sequence_rec(3))(A=1,c=3),b,(0,100))
```

How can I force Sage to compare the elements of the sequence `bool(Sequence_rec(n+1) > Sequence_rec(n)) = true`

for any positive integer n correctly? Thank you for your advice!

Kurt

Thanks for your reply. I forgot to mention that c and k are defined as integers and k<=c. In this case it must be Sequence_rec(n+1) > Sequence_rec(n). I use the elements of the sequence for further calculations. What is the reason Sage is not able to compare symbolic expressions: bool(Sequence_rec(3) > Sequence_rec(2))? It works for: bool(Sequence_rec(2) > Sequence_rec(1))