I am working on a mathematical model looks like this
$$\sum_{t=0}^\infty {A\over e^{(k-r)t}B + e^{kt}C}$$
$k,r$ are fixed real numbers, $k-r$ is positive, $t$ is the index, and $A,B,C$ are non-zero constants.
I feel difficulty find a closed form for that. I try to use integral test to pound it since $i-r$ is positive.
However, I am not able to calculate the following integral:
$$\int_{t=1}^\infty {A\over e^{(k-r)t}B + e^{kt}C}$$
So I wonder whether I will be able to get a closed for my original summation? Could anyone help on this?
Really appreciated!