# 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))

# But Sage computes it is false!

# How can I show that

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