I need some help in evaluating the following limit with assumptions:
Limit[Result, L -> Infinity, Assumptions -> A ∈ Integers && A > 0 && B ∈ Integers && B > 0 && C ∈ Integers && C > 0 && D > 0 && F > 0]
Result := C D (B F)^(A + L) (-C D + B F)^-A ((C D + B F)^(-1 - L) - ((-C D + B F)^(-1 - L) Gamma[1 + A + L] Hypergeometric2F1[1 + L, 1 + A + L, 2 + L, -((C D + B F)/(-C D + B F))])/(Gamma[A] Gamma[2 + L]))
It should come out to 0, and I am sure of this. I just need to verify.
The reason is that I plugged in values for all of the parameters (except L), and then summed over Result from L=0 to L=100000 - the sum converges to 1.
Mathematica is unable to evaluate this limit as I defined it. Is there a proper way?
Thanks in advance for any help.