# 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)

# The following relation has to be true for the defined sequence considering the given assumptions:

bool(Sequence_rec(3) > Sequence_rec(2))

# How can I show that

bool(Sequence_rec(n+1) > Sequence_rec(n)) = true

# Kurt 2 No.2 Revision

# 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 xx


# For the parameters the assumptions are:

assume(A>0,c>0,b>0)


assume(A>0,c>0,b>0)

# The following relation has to be true for the defined sequence considering the given assumptions:

bool(Sequence_rec(3) > Sequence_rec(2))


bool(Sequence_rec(3) > Sequence_rec(2))

# How can I show that

that bool(Sequence_rec(n+1) > Sequence_rec(n)) = true



# Kurt

### 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:

bool(Sequence_rec(3) > Sequence_rec(2))


But Sage computes it is false!

How can I show that force Sage to compare the elements of the sequence bool(Sequence_rec(n+1) > Sequence_rec(n)) = true for the sequence defined? any positive integer n correctly? Thank you for your advice!

Kurt

### 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:

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


But Sage computes it is false!

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 5 retagged

### 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