Obtain the following limit I have to evaluate the following limit:
$$\lim_{n\to\infty} \dfrac{\left(1-\dfrac{k}{n}+\dfrac{1}{n}-\dfrac{1}{2n}\left(c_n-a-b\right)\right)^{n-k+\frac{3}{2}-\frac{1}{2}(c_n-a-b)}}{\left(1+\dfrac{1}{n}-\dfrac{1}{2n}(c_n-a)\right)^{n+\frac{3}{2}-\frac{1}{2}(c_n-a)}}$$
where $a,b,k$ are finite constants and $\dfrac{c_n}{2n}\to x$ as $n\to\infty$.
It's formidable looking, I agree. I get the answer as $e^{\frac{b}{2}-k}(1-x)^{\frac{b}{2}-k}$
However, the given answer is $e^{\frac{b}{2}-k}(1-x)^{\frac{b}{2}-k-1}$. I simply don't understand how exponent of $(1-x)$ involves the extra $-1$.

I get the same result as you. I think the question and the given answer do not match, because if you put $b=2k$, the whole thing becomes $\lim_{n\to\infty}1=1$, while the given answer says $\dfrac1{1-x}$
