I am trying to find how $A$ behaves as $n \rightarrow \infty$ and when the parameters $\mu,\eta,v$ are very small that is near zero. The others like $k_{3}<-1$ and $l_{6}>0 , t_{1},u_{1}$ are constants.
If it is like $(1 + \frac{1}{n})$ it would be easy to think or is intutitve, since I am now handling 4 variables and trying t othink how $A$ looks, it is getting complicated.
I understand that we wll be ignoring parameters raised to powers of $n$, like $\eta^n, \mu^n, v^n$ would be taken to be tending to be zero.
Still I think there must be some way/ theory/ tricky evaluation which can help us to see how $A$ behaves as $n \rightarrow \infty$ and the parameters $\mu,\eta,v$ are small tending to zero.
$$A = -\frac{((a + k_{3}(\alpha + t_{1}v)^n c^n(\eta + 1) - 2)^2 - (a-1)^2 + 4l_{6}(\eta + 1)b - 1)c^n}{4l_{6}c^{2n}}$$
$$a = k_{3}(\eta + 1)b$$
$$b = ((\alpha + t_{1}v)*c)^n$$
$$c = u_{1}v + \frac{1}{\alpha}$$
I am trying to simplify this expression $A$ taking $n$ to be large and $\eta$,$\mu$,$v$ to be very small. The calculation is getting tedious. Any other way of seeing this or source where I can put this and obtaina simplified expression?