Question 150
a) Compute
$$
\lim_{n \rightarrow \infty} \frac{(n^{2}+3) \cdot (n^{2}+5) \cdot \ldots \cdot [(n+1)^{2}+2016]}{(n^{2}+2) \cdot (n^{2}+4) \cdots [(n+1)^{2}+2015]}
$$
b) Compute
$$
\lim_{n \rightarrow \infty}\left(\frac{\sqrt[n]{4}+\sqrt[n]{504}}{2}\right)^{2n}
$$
$$
\lim_{n \rightarrow \infty} \frac{(n^{2}+3) \cdot (n^{2}+5) \cdot \ldots \cdot [(n+1)^{2}+2016]}{(n^{2}+2) \cdot (n^{2}+4) \cdots [(n+1)^{2}+2015]}
$$
b) Compute
$$
\lim_{n \rightarrow \infty}\left(\frac{\sqrt[n]{4}+\sqrt[n]{504}}{2}\right)^{2n}
$$